they get you to either give up banking info, or they send you a fake money order or cheque for a certain amount, and get you to transfer an amount back that is smaller than the amount they supposedly sent, in essence letting you keep your "share". so after you deposit their cheque, you supposedly have the funds to send back to them only to find out a month later that those funds were never real, and you are now on the hook for the amount you sent back. The scam works off the basis that their cheques may take weeks to clear, yet the bank 'gives' you the funds quicker.
Other ways they make money is they ask for 'advances' to help with the process before they can send their dead dictator father's secret stash. In bad cases, they string people along for months or years asking for 5k here and there saying they need the money to bribe an official or something. You never actually get to the big payout portion.
more info here: http://en.wikipedia.org/wiki/Advance_fee_fraud
[Edited 2009-06-24 23:22:13]