The best and easiest way to lower the action is to loosen the strings and shim the neck between the fingerboard and the hoop. Go to your auto parts store and buy a "feeler gauge" set. [ Low cost item ] Start with a .020 thickness and cut that one out of the set. Now slip that one between the fingerboard and the hoop. Tighten your strings up to open "G" tuning and check your action. If that did not lower the action enough, take that shim out and replace with a .030 shim, etc. Keep trying different shims until you get the action where you want it. Good luck.
I'm sure more information is forthcoming, but my understanding is that coordinator-rod adjustment can produce a change in string height, but it's not a recommended solution. I think it'll depend on how much change you are seeking -- bridge height, I think, would be the first option for significant change. Shimming would be the next option. Don't take my word for it though -- listen to these other guys. BM
Chick: Revis's suggestion of the "old tension hoop shim trick" (If I've seen it once, I've seen it a thousand times) is, in fact, the "easiest" and quickest way to make this adjustment. You may, however, discover an unintended consequence; that it deadens the sound of your instrument. I am of the school that holds that there should be no contact of the neck to the tension hoop for this reason. The better location for the placement of that shim is over the upper part of the heel where the lag screw penetrates the tone ring. Gluing a wood veneer shim effectively makes the shim an integral part of the neck. My preference for this fix, which doesn't meet Revis's threshold for "easiest and quickest," is to remove a little bit of material from the bottom of the heel. But this is not a job for a novice. For this you need professional help.
First of all, your neck should not be straight. This usually leads to buzzing. It should have a bow, so that there is about .010-.020" clearance between the 7th fret and string, when the strings are capoed at the first fret and fretted at the 22nd fret. This is called "neck relief". Then you should make sure the head tension is correct, as a sagging head due to the head stretching (seen as low head tension) is probably the most common cause of a beginner complaining about buzzing strings/low action. Heads stretch and need frequent tightening (every month or so).
Only after these things are correctly set should you attempt to modify the action. You can change bridge height, adjust coordinator rods or shim. The shim should be between the upper heel portion of the neck and the rim, as Dick said. Shimming at the tension hoop is a good way to warp a tension hoop, as it binds it solidly. Been there, done that, at least the warping a zinc tension hoop and having to replace it thing.
Please don't stick a shim between the tension hoop and the fingerboard to adjust your neck. That may be the "cheap and dirty" way but you are basically screwing up the fitment of the neck to the pot and putting undue pressure on the tension hoop whose sole job is to tension the head and support a tailpiece, not support the neck. The tension hoop shouldn't touch the fingerboard at all. The only part of the neck that should firmly attach to the pot are where the lags attach to the coordinator rods (called the heel), period. As stated above and if you are a novice use a shim on either the top or bottom part of the heel (depending on too high or too low an action). If you are really adventurous, carefully take some wood off the appropriate areas to adjust. You may also need to remove wood from the fingerboard after the adjustment if it begins binding against the tension hoop. This process may be better left to a professional as you could end up removing too much on one side or the other and thereby causing the neck to not be true and square with the pot when you're done.
Technically , what the above posts have said is true, if you want to get into a job that should be done by a professional luthier. I would not recommend someone removing wood from the neck of a banjo that didn't know what they were doing. What I recommended for you is something that YOU can do that will not hurt your banjo. I have used this proceedure many times on different banjos and never once had any problems with it. If you use a shorter bridge to lower the action it will definately alter the sound of your banjo. Shimming the neck will not.