Strumming is one technique to produce sound with your guitar, finger picking (aka fingerstyle) is another right hand technique. Strumming is a technique where you play all the strings at once with the tip of your finger or with a pick, fingerpicking is a technique where you play the strings one by one.
Let's start with the most simple finger picking pattern:
place your thumb on the bass note of the chord (take Am for this example), finger 1 on the 3rd string, finger 2 on the 2nd and finger 3 on the 1st string (for string and finger naming have a look here: how to read guitar chord charts). Now Pluck the strings one by one: start by pushing the thumb down, then pull the first finger, then the second finger, then the third one.
This technique looks like this (Check the how to read guitar tabs tutorial first if you can't read guitar tablature):
Try to practice this finger picking pattern with a chord progression:
Make sure you finger the entire chord with your left hand and not just the notes you are playing.
Of course you are not restricted to playing the top 3 strings, you can play the other strings as well:
Here's a more complicated finger picking pattern, similar to the pattern used in the song 'Dust in the Wind' written by the band Kansas:
Now start practicing these guitar techniques and chords on some easy guitar songs.
All guitar chord charts © 2010 Dirk Laukens