Craps is centered around the roll of a pair of dice by the "shooter" (a selected player in a traditional casino, the software at an online casino).  Player's can place various bets on the table, and win or lose those bets based on the outcome of the shooter's rolls.  The shooter's first roll can produce 3 outcomes:

• 'a natural' (7 or 11);

• 'Craps' (2, 3, or 12); or

• 'a point' (4, 5, 6, 8, 9, or 10), ie the rest.

Now a nice starting bet in Craps, is a bet on the PASS LINE.  This is done by placing your chips on the Craps table on the area marked PASS LINE before the shooters first roll.  Now with a pass line bet, if the shooter rolls a natural you win.  If the shooter rolls Craps you lose, and if the shooter rolls the point, your bet remains and you win if the shooter rolls the point again before he rolls 7, and lose if and when 7 is rolled before the point.

You can also bet on the DON'T PASS LINE.  This is pretty much the reverse of the above - except you don't win on a 12 for the first roll...the bet is pushed.

You can also bet on the COME LINE after the shooter has had their first roll and already has the point.  This is pretty mush the same as a pass line bet, in that you win if the point is rolled before 7, and lose if 7 is rolled before the point.

Any way, I'm sure you're starting to get the idea.  Here are all the bets sumarised.

• pass line
  1 to 1 pay-out, if the first roll of the dice adds up to 7 or 11, you win. 2, 3, or 12 loses the bet. Any other number becomes the 'point' and if the point is rolled again, you win, if 7 is rolled first you lose. 
  House edge: 1.4%
  

• don't pass
  1 to 1 payout, if the first roll of the dice adds up to 7 or 11, you lose. 2, 3, you win. 12 is a stand off. Any other number becomes the 'point' and if the point is rolled again, you lose, if 7 is rolled first you win.
  House edge: 1.4%
  

• come bets 
  1 to 1 pay-out, basically the same as the PASS LINE except that you must bet after the point. 
  House edge: 1.4%
  

• don’t come 
  1 to 1 pay-out, the reverse of the COME BET, except that a first roll of 2 or 3 wins, and 12 is a stand off. 
  House edge: 1.4%

some other bets...

• odds 
  'taking the odds'
  Once a ‘point’ or a ‘come point’ has been thrown and you have a pass line bet you may bet up to some multiple, usually 2 times, your pass line bet on the 'odds'.  You may take the odds and win if the point or the come point is made before a 7. Pay off is 2 to 1 for a point of 10's or 4's, 3 to 2 for a point of 9's or 5's, 6 to 5 for a point of 8's or 6's. 
  'laying the odds'
  This is the opposite of taking odds, in other words betting that a 7 will be rolled before the point, once the point or come point has been established. Pay off is 1 to 2 for a point of 10's or 4's, 2 to 3 for a point of 9's or 5's, 5 to 6 for a point of 8's or 6's.
  House edge on odds bets are very low - 0.5 to 1% depending on bet
  

• big 6 or 8 
  Here you are betting that either a 6 or 8 will be rolled before the 7, for a 1 to 1 pay-out.  This represents a high house edge bet and is not recommended.
  House edge: 9.1%
  

• place bets
  In craps 4,5,6,8,9, and 10 are known as the "place numbers."  In a place bet, you are betting that your place number is rolled before the 7.  No pass line or other bet on the point is required.  Place bets on 6 or 8 offer the lowest house edge and are recommended (note that odds bets are still a better bet though)
  House edge for 4 or 10: 6.7%
  House edge for 5 or 9:   4.0%
  House edge for 6 or 8:   1.5%
  

• proposition bets. 
  This is simply a bet on the outcome of the next roll. Proposition bets have a high house edge and are not a recommended play.  Odds are as follows:
  2 or 12 pays 30 to 1, House edge: 13.9%
  3 or 11 pays 15 to 1, House edge: 11.1%
  7 pays 4 to 1, House edge: 16.7%
  Any craps (2, 3 or 12) pays 7 to 1, House edge: 11.1%
  Field ( 2,3,4,9,10,11, or 12), even money for (3,4,9,10,11), 2 to 1 for (2 or 12) House edge: 5.5%