Familiarize yourself with the picking hand position. Your thumb rests on the low E string (it should also be ready to pick the A string) and the index finger rests on the D string (it also must be ready to cover the rest of the higher strings). Your three other fingers should rest on the pick guard, along the edge of the sound hole.
Walk the bass line, using only your thumb for picking. While you are walking the bass line, use your index finger to play the treble notes -- this completes the chords whose bass notes you pick with your thumb. When strumming chords, use your thumb and the tip of your index finger.
Listen to recordings of finger-style guitar players and try to emulate their sound. This will help you get used to the timing and rhythm. Notice the way this picking technique alternates between bass notes and higher notes (thumb and index fingers). This alternation is important to get used to, as it is the foundation of two-finger guitar playing.