When your opponent starts advancing a pawn (even better - before that), you should try to find out what that move's purpose is. There are some possibilities:
- gaining space - the squares behind the pawns are usually better protected by the side that owns the pawns, especially in positions where the center is closed, hence that side's pieces have more space to maneuver and prepare for attacking or get better development, while the opponent's pieces at that side of the board may be hindered;
- opening lines - after exchanging pawns, the heavy pieces will be able to get to the files where the pawns were and be more active, also diagonals may open up for the bishops / queen;
- creating pawn weaknesses / strong points - outposts (squares protected by pawns that are unattackable by opponent's pawns), holes (squares the opponent can't control with a pawn), backward / isolated / doubled pawns, and so on - all of which can be used as strategical features to base subsequent play upon;
- breaking up the opponent's king's protection (by either creating pawn weaknesses or driving defending pieces away) - like the prevoius, but with the purpose of an attack on the king.
In all cases, you should try to understand the purpose(s) of such moves, and ideally be able to anticipate dangerous ones and prevent them, or defend properly. You may defend by avoiding the pawn exchanges (making it unfavorable for the opponent to try to exchange), blocking those pawns' advancement, creating threats or counterplay (there's a general rule that if your opponent attacks on the kingside you should try to open the center and attack there; kingside attacks are usually more successful with a closed center so that the opponent has fewer counterplay and it's more difficult for him to exchange pieces or gain space with pawns - but of course it matters on the position), sacrificing material to stop the attack (but only if necessary - otherwise your opponent may simply reorganize and attack somewhere else, having material advantage), or by preparing to exploit the resulting position (getting your rook(s) oth the file to be opened, using opened diagonals or weakened squares in your opponent's position), etc.
Amateur questions, but I always have problems breaking up pawn rushes, particularly when the opponent (black or white) will castle and immediately push their kingside pawns forward into my kingside castle. The best solution I've come up with, which rarely works, is to sacrifice a knight or a bishop for a couple of pawns to break up the momentum. Does anyone have a better suggestion/tactic?
I almost always open Queen's Gambit for White and French for Black