Hold the instrument on your lap (don't hug it tight or you'll deaden the sound), or get a strap and adjust it so
that your right arm (plectrum arm) is horizontal from the elbow.
Find a pick (plectrum) that you are comfortable with (light to medium is normal but it's a matter of preference -
try several different grades).
Hold the pick lightly but firmly resting on your first finger between the first and second joints and clamp it with your thumb
(pointy end towards the strings!).
The Bouzouki (in Irish music) is mainly an instrument for accompaniment although melody runs can be quite effective.
Going to local sessions is a good way to learn. The tunes get into your head and you start picking them out after a while.
Listening to tracks (The Bothy Band is essential listening) of the tunes you'd like to play is good for this too.