Up in pawns, down in pieces?


Generally speaking, yes, side with pawns tries to trade down to get an endgame with an active king and pawns that are hopefully connected and advanced, but not blockable. If the side with only a piece can form a blockade and create a passer and/or win the pawns while still retaining a queen able pawn, he should win.

Really depends on the position.
Are your 3 pawns connected? Are their weak? Are they all isolated? Are they restricted?
The side with a piece up should try to freeze majorities (if there are any) because a well executed pawn storm could easily steamroll you and as many said, try to use the extra piece in the attack wether it is on the king or in the queenside.
The side with the 3 pawns should try to push those majorities, specially if they do not compromise king safety. Reaching an endgame is probably a good idea.
What should you do if you're up in pawns but down in pieces? I had a recent game where I was on the opposite side of that equation: I was up a bishop but down three pawns, so technically even material. My opponent threw all his pawns at me, but that just exposed his king and allowed me to make a checkmating attack. What should I do if I find myself in his situation?