Having recently attended a song circle, it occurred to me that learning how to pick up what someone else is playing and being able to follow it reasonably quickly is a basic art for which there are some skills, some of which are learned over time, but for which there may be some useful tricks that might be suggested by the experts here.   A few that come to mind:

1) Get used to telling people what key you are going to be in. Maybe this will rub off on others and save time!
2) The basic idea is to figure out the key the other person is playing in, learn to follow the chord shapes that other people are using (here i am thinking of the guitar), of which the big one is the chord used to start the song which, unless the sound is minorish, is likely to be the I chord, or the tonic.
3) The chances are pretty good that in folk songs you will get the I, IV, and V chords of the key. If there is a minor chord it will likely be the VI chord (Am in C, and so on).
4) The G chord and the C chord are usually easy to recognize, though it can be hard to distinguish between the C chord and the F. If the person is using a bar chord on the first fret, it is a pretty good bet it is a F.
5) Many people use capos, and play the shapes of different keys. You need to be able to count up the frets and figure out again what the first chord of the tune is.
6) It takes a while, but you should learn how to hear when the song is heading for the dominant (V) or the final tonic (I), this gives you a clue as to what to expect from the fingering ahead.
7) Three other patterns of sound to learn are: (I, I-7, IV), the 12 bar blues, and the jazz standard, II-VI-II-V-I);
8) Play quietly until you get it right!!!!!

Other tricks of the trade?

yours,

Peter T.