Assign your fingers to the correct strings. Use your thumb for the three lowest-pitch strings of the guitar, being E, A and D. Only use your thumb for these three strings when finger picking. Next, use your index finger for the G string, middle finger for the B string and ring finger for the high E string. Your smallest finger is not a part of standard guitar finger picking.
Keep your hand relaxed over the strings. Let your hand line up properly with the finger assignment. Place your thumb in a comfortable position so that it can freely alternate between the E, A and D strings. Let your hand and wrist be static so your fingers do most of the work.
Practice finger picking simple arpeggios. Put your fingering hand into the shape of a D major chord. Practice a basic up and down finger picking pattern. Use your thumb to strike the D string, index finger to strike the G string, middle finger to strike the B string, ring finger to strike the E string. Repeat this step up and down while slowly increasing speed as you become more comfortable. Repeat this step using several different chords and patterns to practice.
Combine finger picking various strings to produce chords. Form the shape of any chord and pluck the dominant notes. For example, make a C major chord with your fingering hand. Next, use your thumb to strike the A string, your index finger to strike the D string, middle finger to strike the G string and ring finger strike the B string. Pluck all of those strings at once to produce a chord.
Learn a finger-picking song after mastering the basic exercises. Using standard guitar tablature, the fingers go with letter labels such as P for thumb, I for index, M for middle and A for ring finger. Practice the song one passage at a time with a metronome and using the proper fingers for each string. This will ensure good technique and quick advancement if your finger-picking journey.