Fingerstyle Guitar...

 

The basis for most fingerpicking or fingerstyle guitar is the development of independent movement in your right hand thumb and fingers so that you can play a rhythmic bass line on the lower strings and a melody at the same time on the top strings.

there are countless subtleties and variations in more complicated fingerstyle playing, but, initially it is better to stick to basic pieces where the thumb plays the bass line and the fingers play the melody.

Much of the music that features American fingerstyle is 4 beats to the bar (measure).  usually the beats contain alternating bass notes.  These alternating bass lines are somewhat of a trademark in folk and country music but rarely seen in classical or other advanced fingerstyles.

The right hand technique can vary somewhat depending on the musical style and whether the guitar is steel string or nylon. But generally the edge of the palm rests on the top of the bridge.  This provides a steady anchor point and allow you to dampen the bass strings do that they do not ring throughout the melody line.

the "Clawhammer" is an American fingerstyle made famous by the Reverend Gary Davis and is popular in acoustic blues.  It gets its name because the right hand looks something like a claw hammer used to pull out nails.  The thumb plays the bass line with down strokes and the first two fingers play the melody with up strokes.  Some guitarists use three fingers and there are infinite variations.  At the end of the day, the style is not as important as gaining thumb and finger independence.  To do that you need to start with basic patterns and then gradually add difficulty.