OK - everyone is pretty correct up above, I just wanted to pop it all together in one nice neat post to get all of the info in a tidy package here.

When you see three notes, four notes, whatever and they are tied together with a slur (what would look like a sideways parenthesis mark), they are played legato. In other words... smoth/none to little pick attack. Most often than not, legato means hammering on and pulling off. There can be legato picking runs, but typically it means to hammer/pull.

That being said, technique-wise...
Pick the first note
Hammer on the next note
Wash, rinse, repeat.

You will notice that the strength required to get clear legato phrasing and the accuracy required may make it seem impossible. Quite frankly, your first attempts will sound pretty trashy. Keep up with any finger exercises your instructor has given you or any of the exercises here on the site and you will build the finger strength and accuracy to pull off some nice legato runs.

32nd notes... I count them as 16ths (one - e- and -a) but I double up the pick attack or the left hand legato attack. I can never stress enough the importance of working with a metronome... :-)