There are at least four casino workers at a craps table at all times.
The boxperson oversees everything while seated at the center of the table with lots and lots of chips stacked in front of him. He settles disputes, counts the money, and generally makes sure things are running smoothly. He also watches the dealers to make sure they're paying off winnings (and taking in losses) accurately. If it is especially crowded and especially large bets are being placed, there may be a boxperson at each side of the table.
There are three dealers at each table (actually, four dealers are assigned to each table, but they rotate so that one is always on break). Two of the dealers stand on the back side of the table facing the players -- these are "on base," meaning that they are the ones who keep track of your bets, pay you if you win, and take your chips if you lose. The dealers on base also place your bets for you if you are making certain types of bets (for example, Place bets and Come/Don't Come bets are placed by the dealer -- more on these later) and mark the "point" with a marker called a "puck" once the point has been established (more on points later).
The third dealer is called the stickperson. The stickperson uses a stick (also called a "mop" or a "whip") to handle the dice, moving them from the back wall to the Shooter after each roll. The stickperson is said to be the dealer "on the stick." He doesn't usually deal directly with the players except for moving the dice to them (and occasionally placing bets for players in his area). The stickperson is also the one who talks up the game, encouraging players to place higher bets or to place bets where the casino has a bigger edge. (Watch out for those -- don't get sucked in by the stickperson's banter!) The stickperson can really influence the bets on the table. Talking up the dice when a good roll is going can increase the amount of money being bet -- usually increasing the casino's profits considerably.