Texas Banjo posted a good explanation of vamping on BHO the other day. I don't remember exactly where or I'd give you more complete directions on how to find it. However, vamping is a means of providing fairly unobtrusive backup. It is usually done on the off-beats (the two and the four.) Typicallyyou'd use the thumb on the 5th string on the one and three beats and on the two and four, you'd use the thumb, indiex and middle to hit the 3rd, 2nd, and 1st strings. The trick (and the difficult part to learn) is to damp the strings after picking them by slightly lifting the fretting fingers of the left hand. Like many things, you can learn the basics in an afternoon and spend half a lifetime refining 'em. Hope this helps.
Vamping isn't music theory, it's a technique of playing rhythm. Since vamping is done all types of instruments and banjo styles please, what style of banjo playing are you looking to learn how to vamp.
Hugh Playing since 1964
"If the banjo was any good, The Beatles would have used it."- Bill McEuen
The above works just fine IF you're in 4/4 time and counting one beat per click. Just be sure that you're vamping on the OFF beat -- and with a metronome, you can get confused sometimes and miss a beat and then be vamping ON the beat.
That is, as said above, pick the 4th string on the 1st beat, do a 2 finger vamp or "pinch" on the 2nd beat, pick the 4th string on the 3rd beat and another 2 finger pinch of the 4th beat. That way you'll get used to vamping on the off beat. After you get familiar with the technique, just drop the pick on the 1st and 3rd beats and you'll have a great vamp.
Also, when vamping, you need to "damp" the strings -- or, when you do your pinch, then let the pressure off the strings so they don't ring. That takes practice to make it sound right so don't get hung up on trying to make it sound perfect, just be aware that eventually you'll need to learn to "vamp with a damp".