You could try throwing an E7 before the Amin chord.

Am, Dm, Emajor.

The "relative minor" is no longer operative.  Fmajor would be triad using the same scale notes as A minor, although the flavor of the chord would sound different.  Can experiment with various F and F# chords to get the sound you are looking for.

If you're talking about playing the song in the key of G and then continuing playing and start playing something in the key of Aminor, this is called "modulation."

As Sunrise Lee noted, the usual pivot chord would be E or E7, just before the Aminor.  The question is, how to get to E?

For simple folk/country tunes, often the sequence is G  E7  Am.  Go directly from G to E the pivot chord.

Other ways may go a longer route, such as G  D  E7  Am.

How the sequence of chords is "voiced" -- meaning mostly what we hear as the high note and the low note -- affects how the smoothness of the transition is hear.

While a classical composer may go through several connecting chords on the way from G to Aminor, we usually don't hear this in popular music.

I must not be making my thoughts clear. For an example, I want to take a song that is in the key of G, and uses the chords G, C, D, Em. To convert the song to the key of Am, I would switch all G chords to Am, but what would the other chords be switched to??

I don't pretend to be an expert on anything but from my guitar playing days If I wanted to use Am as a key [tonic] I would use E7 [for the dominant 7th] and Dm [Dminor as the sub-dominant]. We thought of chord progression in terms of tonic [Am], dominant [E7], and sub-dominant [Dm]. Music across guitar genres is so different that this nomenclature may not be acceptable but it should work out musically.

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Originally posted by Ybanjo

I must not be making my thoughts clear. For an example, I want to take a song that is in the key of G, and uses the chords G, C, D, Em. To convert the song to the key of Am, I would switch all G chords to Am, but what would the other chords be switched to??

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Ybanjo, it seems like you are asking to reharmonize the song from the key of G to Am.  Depending on your level of theory I'm not sure the answer will be simple or not.  Changing from a major key to another major key is simple, changing to a minor key is a little more involved but can be a fun exercise.  So just for clarity are you looking to use the same melody over a minor progression?  It will change the flavor of the song a bit.

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Originally posted by Alex Z

Am, Dm, Emajor.

The "relative minor" is no longer operative.  Fmajor would be triad using the same scale notes as A minor, although the flavor of the chord would sound different.  Can experiment with various F and F# chords to get the sound you are looking for.

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This...

If you didn't want to change the melody (scale steps), you could play the melody in the Key of F, and use a progression like Am Gm Edim F.  There are other chords you could use as well.

Alex already mentioned the chords: G becomes Am, as you also already mentioned, C becomes Dm, and D becomes E major. The Em becomes Fm as far as I'm concerned, I tried it with Travel On and it worked. Try it with your song. The harmonic feel changes quite a bit with the minor shift, but I believe those are the chords properly transposed.

If you just want to transpose

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Originally posted by sean curran

Alex already mentioned the chords: G becomes Am, as you also already mentioned, C becomes Dm, and D becomes E major. The Em becomes Fm as far as I'm concerned, I tried it with Travel On and it worked. Try it with your song. The harmonic feel changes quite a bit with the minor shift, but I believe those are the chords properly transposed.

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Depending on the melody it isn’t that simple.  If you are playing the melody as written in G major (harmonized) then Dmin, E, and Fm would be outside of the harmonized scale and the notes could clash.

If you changed the key from G to the key of  Amin then you might have to change the melody to accommodate the minor 3^rd of the one chord as the original melody could be derived from the major aspects of the G major chord.

The way that I arrived at the chords was basic reharmonization of the G major chord progression.  I used Bm Em F#dmin G.  Bm (III chord) would work as the first chord in this progression as it has the same notes as its triad as the top three notes a harmonized Gmaj 7 chord has.  G major 7 would be spelled G, B, D, F#; Bm would be spelled B, D, and F#.  They have the B, D, F# in common. The melody would fit over the Bm chord because it worked over the G major chord.  And so on with the other chords of the progression.

Using that logic I looked at what major scale contained Am as the III chord, F major, and used the same chords steps from within that scale to get Am Gm Edim F.  So if you wanted to play in the key of Amin (Phrygian in this case) and keep the melody exactly the same from a scale step perspective this would work.  Just play the melody as written in F.  Of course, there are also other substitutions you could make, as I said this is basic.

This would allow you to change a song in the key of G, and uses the Chords G C D Em, and convert the song to the key of Am without altering the scale steps in the melody.

It's been a slow day at work ??.  I’m enjoying the discussion.

If you transpose the melody from G to Am, then you are not under any circumstances looking for chords that belong in a harmonized G major scale. You'd only be doing that if you hadn't transposed it.

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Originally posted by sean curran

If you transpose the melody from G to Am, then you are not under any circumstances looking for chords that belong in a harmonized G major scale. You'd only be doing that if you hadn't transposed it.

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Correct.  I'm saying that you may have to change the notes in the melody (scale steps) if you go from the key of G to Amin.

It might be easier to first think of how would you change the song, keeping the same tonic... as from G major to G minor. Then transpose after (say up 2 to A)

Basic way is just going by scale difference, flat third, sixth, seventh. This can be applied to melody; and chords. Changing G/C/D/Em (I, IV, V, vi) to Gm/Cm/Dm/Eb. (then can transpose that all up 2 frets to A)

That said it might work that well musically.

I just tried this with "Wagon Wheel", and found this to be pretty good:

Am E F Dm
Am E Dm Dm (where each chord symbol represents one measure).

Well, obviously my wish for a simple solution isn't possible. I was hoping for some sort of straightforward transposing of chords. Not the case, unfortunately. I have a small understanding of music theory but am lost on most of these discussions. I've known other players to play a song in a minor key and just wanted to be able to do that. First song I remember hearing was "You Are My Sunshine", played in Am. Very haunting sound.

Guess I need to just forget it.

"assume we're talking about a tune that has 3 chords plus the relative minor G,C,D,Em for instance. How do I change the key to Am"

"my wish for a simple solution isn't possible. I was hoping for some sort of straightforward transposing of chords"

Not only is it possible, the answer has already been given!  It was a simple question, and it has a simple answer.  

"Am, Dm, Emajor.

"The "relative minor" is no longer operative.  Fmajor would be triad using the same scale notes as A minor, although the flavor of the chord would sound different."

Play in A minor in good health!  

I admit that I'm not very skilled at music theory, and I still don't understand how C becomes Dm or D becomes Emaj.

I used the chords in the key of G just as an example, but ideally I would love to be able to shift any key to a minor. At this point I'm not getting it well enough to do that. Suppose I wanted to transpose to Gm instead?? Sorry but I just don't get it yet.

To understand transposition , it helps greatly to first understand intervals and scales.  Triad chords are built from that.

I don't think that one can get all that information from posted replies, since replies tend to be more how each person understands, rather than an organized sequential presentation of knowledge. 
 

Wish I had a "learn it yourself" theory book I could recommend, but all my books were part of music school courses and they take some direction and time to decipher. 
 

Maybe others might have a recommendation. 

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Originally posted by Ybanjo

I admit that I'm not very skilled at music theory, and I still don't understand how C becomes Dm or D becomes Emaj.

I used the chords in the key of G just as an example, but ideally I would love to be able to shift any key to a minor. At this point I'm not getting it well enough to do that. Suppose I wanted to transpose to Gm instead?? Sorry but I just don't get it yet.

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Your original question was transposing the song key (G to A); and changing the mode (major to minor); which are 2 separate functions. As I answered changing from G major to G minor; but I'll try break down a little more  When looking at a key/mode scale... note the difference of  whole step and half step spacing in major vs minor. For chords, can also count and assign those 1 thru 7, based on the root's scale step. To harmonize the chord; helps to know how chords are made), to decide if major or minor can initially just follow the notes that belong in the scale (though chord tones can deviate from scale).

how C becomes Dm 

In key of G major, the C (maj) is the fourth chord.
In key of G minor fourth chord would be a C minor;
Transpose that up from G to A, and the fourth chord becomes a D minor.  

D becomes Emaj.

Similar, but a little different. 
In key of G major, the D (maj) is the fifth chord.
In key of G minor fifth chord would be a D minor (or D major);
Transpose that up from G to A, and the fifth chord becomes a E minor (or E major).

The fourth chord becomes In key of G minor because the G minor scale has an Eb note rather than an E note. One thing might notice in this latter part of fifth chord is a little difficult to explain in brief post. If look scale notes of minor mode, seems like at the fifth chord should be minor (F note in key of G minor; so Dm); and you could use that. But often folks find it just fits better to keep the fifth chord as major. Without going into long explanation of why, can just listen and decide which you think fits best; which is what it comes down to... how it sounds; what pleases the ear.

It's extremely difficult to learn common music theory from only written materials.  Notes and chords have have functions, not just names, and hearing how the functions work is basic learning tool.

Can't learn to play a banjo from a book without hearing the notes.  Can't understand music theory without hearing the intervals, scales, and the functions of notes and chords.

I think the crux of the matter is that if you simply play minor versions of the chords, you will have to adjust the melody to fit the altered scale. The third and seventh notes (B and F#) in the G major scale would need to be flattened to form the G minor scale, but depending on the song those notes might not be that prominent in the tune.

An alternative is to try the relative minor key to G, which is Em, where the notes of the scale are unchanged from G major, but start and end on the E note rather than G. That maybe what you have heard others doing.

If you are just after a different, more archaic sound, then you could try playing out of sawmill tuning (gDGCD), but stay in G major. They call this Mountain Minor because it is neither major nor minor, but sounds like a minor, though you have to slightly alter the chords to take account of that recurring c note on the b string.

Most of us assumed the OP had meant altering the melody from major to minor; (then transpose up a step).

What Jerry Hatrick mentioins is valid point, as a possibility, that you could simply reharmonize with alternate chords; thus giving a minor feel; I have done that and can work. But overall not necessarily simpler or as straightforward. (nor understanding explanation why)

Certainly is the case; on some tunes, (like mentioned You are My Sunshine) might be able to just fill in relative minor(s), the I chord the relative minor vi; might give a bit of that. However, on many songs it might actually be even more complicated, involves more theory understanding, as the melody would involve more non-chord tones and/or make for more complex chord extensions and progressions.

For example, lot of major key have strong fifth notes; right away that makes the home chord relative minor a 7 (if was G; now Em7). As go through melody, similar issues, and while might find chord that works sort of, might also take away from feel of progression. As Ira pointed out, notes and chords having functions (not simply what can fit, math works out)... part is the function of movement, cadence, and resolve.

"You Are My Sunshine" in G major.

You are my (G) sunshine, my only sunshine.

You make me (C) hap-pee, when skies are (G) gray.

You'll never (C) know dear, how much I (G) love you.

Until you (G) take my (D) sunshine a-(G)-way.

"You Are My Sunshine" in A minor.

You are my (Am) sunshine, my only sunshine.

You make me (Dm) hap-pee, when skies are (Am) gray.

You'll never (D) know dear, how much I (Am) love you.

Until you (Am) take my (Emajor!) sunshine a-(Am)-way.

That's how G, C, D chords in the key of G major become Am, Dm, E chords in the key of A minor. 

Now, you need to sing the melody of the song in A minor too.  Can't just sing it in A major, or G major, or G minor, or B minor, or E minor.

As mentioned, it is difficult to understand this without hearing it.  If you could hear it, would take 90-120 seconds to understand how to sing it in A minor with the A minor chords and what the principles of the chord changes are between G major and A minor.

In fact, since the poster is familiar with this song in both major and minor, maybe fool around a bit on the banjo to first get the G major chords and sing it in G major, and then change to the A minor chords and figure out the sung melody in A minor.   To paraphrase an old saying, "a note heard is worth a thousand words." 

I was working on Autumn Leaves song yesterday. It's in Am and I played it in open G tuning using Am chords. Works just fine. You do have to figure out some new chords if you're not used to them. Dm is easy to finger IF you know what the chord is.

You guys have given me a ton of information. Not sure how much I fully understand, but I'm trying to read each post carefully & understand as I go along. As of now, I still can't figure out how to convert a song in any major key to any minor key. It's obviously much more complex than I was hoping. And it might be easier than I'm initially thinking right now. Obviously I need to study it much more.

Thanks for all the responses. I knew there were some serious musical folks on here.