There are several different styles of fingerpicking. They each have a specific pattern of fingers plucking specific strings. A good pattern to start with is Thumb and Index, TI, back and forth. This gives you two different strings sounding on each stroke. Most folks also change the Thumb or the Index each time to generate a four-stroke pattern.
Finger: T I T I T I T I or T I T I T I T I String: 4 1 4 2 4 1 4 2 or 4 1 3 1 4 1 3 1
The first pattern alternates the Index finger between strings while leaving the Thumb on the same string. The second pattern alternates the Thumb on different strings.
Try these patterns on your favorite chords to see how they sound.
You can also add a third digit, the Middle finger.
Finger: T I T M T I T M or T M T I T M T I String: 4 2 4 1 4 2 4 1 or 4 1 3 2 4 1 3 2
Finger: T M T I M T I M String: 3 1 5 3 1 5 3 1
It takes advantage of the short 5th string to make a neat-sounding syncopation. You can also use these rolls on any other instrument. If you want that sound on the banjo, you’ll need to study Bluegrass-style or Scruggs-style fingerpicking. Youcan use the same finger pattern: TM TI TIM on different strings, and you can mix it up doing TIM TM TIM or TIm TIM TM.