By learning to use the fingers of your right hand to play individual strings, you will open up a wide range of musical possibilities. Fingerstyle can add sophistication and variety to any style of guitar playing and it has the added benefit of being fun!
 

The following abbreviations are used for the right hand fingers: p – pulgar or thumb; – indicio or index finger; m – medio or middle finger; a – anular or ring finger. In standard fingering you will use the thumb (p) to play the lower three strings, the index finger (i) to play the third string, the middle finger (m) to play the second string and the ring finger (a) to play the first string.  There are two other common fingerings and, of course, lots of exceptions to each, but concentrate first on standard right hand fingering, which you will use most often.
 
Begin by getting used to the feeling of striking the strings with the appropriate fingers. The fingers of the right hand should be curled and almost perpendicular to the strings. If your fingers are pointing toward the neck of the guitar, you can correct the position by putting your fingers in place (one finger per string) and, without allowing them to move on the strings, sliding your thumb toward the head of the guitar until the fingers are pointing downward instead of sideways. This position will allow you to strike the string with a natural action of the last joint, rather than having to use an awkward and inefficient, whole-finger motion. If you are playing an acoustic guitar, be certain that your hand is positioned over the sound hole. A bit of fingernail will enhance your sound and make it easier to fingerpick. Keep your nails rounded for the best sound.
 
Here is an exercise that you can use to practice your fingerpicking:

                                          (string numbers)  II:  6   3  2   1      5   3  2    1     4   3  2    1  :II 

           The fingers you use will be:                p   i   m  a ;    p    i  m   a ;   p  i  m   a 
 

When you hold down a chord and play one string at a time you are playing an arpeggio, or broken chord. Remember that the ring finger is used to play the first string, the middle finger to play the second string and the index finger to play the third  string. Practice slowly, until you can play the notes evenly and clearly as eighth notes.

Fingerpicking patterns
Next, you will learn to play two accompaniment patterns. The first pattern is one that you will use for songs in 3/4 time. As in the exercise above, the numbers indicate string numbers. The letter “B” will stand for the bass note (string 4, 5 or 6), which will vary according to the chord. Whenever possible, use the root of the chord as the bass note. For example, you will use the sixth string as the bass on a first position G chord, because when you hold down the notes for the first position G chord, the note on the sixth string is G. First position E chords will have a sixth string bass, C and A chords will have a fifth string bass, and D chords will have a fourth string bass.

Strings:  B 3 2 1 2 3 
Fingers: p i m a m i

Count:  1 & 2 & 3 &

The next pattern can be used for songs in 4/4 time. In this pattern you will play the first and second strings at the same time:
 

                                                                    Strings: B 3 2 3 B 3 2 3
                                                                                           1            1

As in the previous pattern, the notes should be even eighth notes (1 & 2 & 3 & 4 &). When you are comfortable playing these patterns with the root of the chord as the bass note, you can begin alternating the bass. For example, you can alternate between the sixth and fifth strings on a G chord or the fourth and fifth on a D chord.