Craps is an impressively convoluted system of bets surrounding a pair of sixsided dice. Although A Fever on a Crappy Day gives an overview of the basics, there's a bit more to craps.
The Gameplay
The gameplay itself is a bit more involved than the come out rolls, but that's where it starts: the shooter throws the dice until a 4, 5, 6, 8, 9, or 10 hits. When that happens, the "point" is then established, and the shooter continues throwing until either the point or a 7 hits. If the point hits, then shooter comes out again; but when the 7 hits, all bets on the table are cleared and the dice pass to the next player.
As a quick example: a shooter's round could work like this:
 Come out: 3, 7, 7, 12, 5
 Point (5): 12, 3, 4, 6, 5
 Come out: 11, 4
 Point (4): 6, 8, 7
The shooter's first point was 5 (which she then made), and the second point was 4 (which she didn't make). This goes on indefinitely.
The Bets
The fundamental bets in craps are the "line" bets, the two key ones being "pass" and "don't pass". They're placed before a come out roll, and pay even money (1:1).
On the come out, a pass bet immediately wins if a 7 or 11 hits, but immediately loses if a 2, 3, or 12 hits. After the point has been established, the pass bet wins if the point hits, and loses if the 7 hits.
A don't pass bet is almost the opposite; on the come out, it immediately loses if a 7 or 11 hits, but immediately wins if a 2 or 3 hits, and pushes (doesn't win or lose) if a 12 hits. After the point has been established, the don't pass bet loses if the point hits, and wins if the 7 hits.
Back to our example:
Pass  Don't Pass 



The push is the house edge for line bets.
More Bets
There other line bets in craps are "come" and "don't come" bets; these work similarly to the pass/don't pass bets, except they're placed after the point has been established and they effectively establish their own point that must hit to win, independent of the primary point.
For example, consider the second set of rolls (when the point was 5). Placing a come bet on each of the numbers would result in a Lose, Lose, Win, Win, Lose. The first two bets are lost immediately when the 12 and 3 roll; the 4 wins during the second come out, the 6 wins in the last round, and the 5 loses on the last throw.
Although line bets pay even, gamblers can increase their overall odds by purchasing, well, odds. These are multipliers of the original line bet and have no house edge; that is, they pay true odds of 2:1 (for 4 and 10), 3:2 (for 5 and 9), 6:5 (for 6 and 8) on the pass/come, and the inverse when betting the don'ts. Casinos will limit odds anywhere from 3x to 100x the original bet.
Even More Bets
There are a dozens of different singleroll bets; i.e., bets that are played anytime and win or lose depending on what hits. The common ones are:
 Singlenumber bets that win only if a specific number hits: 2 (pays 30:1), 3 (15:1), 11 (15:1), and 12 (30:1)
 Multinumber bets win if any number in a certain set hits: 2/12 (15:1), 2/3/12 (7:1), 2/3/11/12 (7:1 on 11; 3:1 on rest), 2/3/4/9/10/11/12 (2:1 on 2, 12; 1:1 rest)
 Combination bets win if the dice roll a specific combination of dice: X+Y (15:1) , X+X (30:1)
And then there are also plenty of multiroll bets available.
 Hard ways: a bet that a 4, 6, 8, or 10 will hit as an identical pair (e.g. 3+3) before either a 7, or that same number will hit as a mixed pair (1+5, 2+4); this typically pays 7:1 (for 4 and 10) and 9:1 (for 6 and 8)
 Place: a bet that a 4, 5, 6, 8, 9, or 10 will hit before a 7; these pay 9:5 (for 4 and 10) , 7:5 (for 5 and 9), and 7:6 (for 6 and 8)
 Lay: a bet that a 7 will hit before a 4, 5, 6, 8, 9, or 10; while these pay true odds  1:2 (for 4 and 10), 2:3 (for 5 and 9), 5:6 (for 6 and 8)  a 5% commission (rounded to the nearest dollar) is paid on the winnings
As important as the bets are, the nicknames are equally  if not more  important. Each specific roll can have multiple nicknames  nina (9), fever (5), yo (11), box cars (12), Charlie Sheen's breakfast (12) – as can all of the various bets – penny any ($1 on a singleroll 2/3/12), nickel hard strong ten ($1 on hard 4, 6, 8, $2 on hard 10).
Jackpot Bets
And since these clearly aren't enough options, casinos have started introducing multipoint jackpot bets. The Fire Bet™ (yes, of course it's trademarked) is a bet that the shooter will make four to six different points before seven'ing out, and it pays 25:1, 250:1, and 1000:1 after the forth, fifth, and sixth point hit.
##
Phew. I feel you should get extra credit for just reading through these requirements, though I can only imagine the convoluted ways to implement these requirements. Good luck.