One of the most useful and popular fingerpicking patterns is called Clawhammer.
The basic clawhammer pattern is:
Here is the clawhammer pattern applied to a C chord.
Once you are confident playing this pattern apply it to other chords as in the next example.
In bars 7 and 8 the open third string is used as a bass note and played by p on the 2nd and 4th beats.
Use this clawhammer pattern to accompany the melody of the song Marianne, which is a Caribbean folk song.