The player in the position immediately to the left of the dealer (that is to say, clockwise) posts an automatic bet called the small blind, and the player immediately to his left (or two places to the left of the dealer) posts an automatic bet known as the big blind. These are forced bets that players must make in order to get dealt into the game. All other players get to see their hands "for free."
Players decide whether to play or fold (quit) in a clockwise position, starting with the player immediately to the left (clockwise) of the big blind. Any players who fold are no longer eligible for the pot and are skipped over in subsequent betting rounds for that specific hand.
In Hold'em, your position relative to the other players is critical. When you're in the beginning of the betting order, your cards have to be of higher quality than the cards you would normally play in later position — especially if lots of players are left in the hand — because you have no idea what evil may lurk beyond.
Likewise, if you're riding at the back of the calling order, you can afford to play looser hands (those that aren't as high quality) and hope to catch cards to break people's dreams. In fact, pot odds (the amount you bet relative to the amount you would win) say that sometimes you should call, even when you have a lesser hand.