The most common bets on the Craps table are the Pass Line with Odds, Place bets on the 6 and 8, and possibly some Hardways. If you learn these few bets then you'll be able to play with everyone else while having a decent understanding of the game.
The Pass Line bets that the shooter is going to establish a Point and will roll it again on before they roll a 7. Most players at the table bet the Pass Line so everyone wins and loses together. It's the same fate that bonds all the players at the table.
Come bets are like small Pass Line bets. They win on 7 or 11 and lose on the 2, 3, or 12. Otherwise, the Come bet moves into a Point and that Point needs to be rolled again in order to win.
The Hardways bet that the points 4, 6, 8, or 10 will roll as a pair (Hard). If any of those numbers roll as anything other than a pair then they are considered to have been rolled 'Easy'.
The Eleven is called a Yo because Eleven sounds like Seven and you don't want to mix up the two.
Bet the don'ts. They are the Don't Pass, Don't Come, and Overlays. All of these bets need the 7 to roll which makes the shooter, and usually the rest of the table, lose.
Everybody at the table has an opportunity to throw the dice. The current shooter continues to throw the dice until they don't make their Point (7 Out). Once they 7 Out the bowl is dumped and the dice are passed clockwise to the next person.
The Boxperson is there to make sure the game moves along smoothly. They make sure the dealers are doing their jobs correctly, solve disputes, and service players.
If the dice go off the table the Stickperson will dump the bowl and offer the shooter the remaining dice. If the shooter wants the same die that rolled off the table they will have to tell the dealer "Same dice" before the dealer dumps the bowl so be quick!
The Pass Line with Odds and the Don't Pass with Lay Odds are the best bets on the Craps table. Place bets on the 6 and 8 are the best followed by the 5 and 9 then the 4 and 10. The Field is surprisingly not a bad bet. If it pays triple on the 12 then it turns into a really good bet.