Quote from JackR:
One of two things happen:
1) The FDIC arranges for another bank to take over all accounts at the failed bank. This is typically done on Friday night. On Monday the new bank is in place and you have an account with them.
2) The FDIC has not been able to get any other bank to buy the failed bank. FDIC sends you a check for your funds.
Understand that the FDIC only insures up to $250,000 (it may revert to $100,000 in 2014). Anything over $250K becomes part of the bankruptcy and how much you recover depends on the outcome of the bankruptcy. When you get the adjusted amount (if anything) is a function of the bankruptcy as well.
If you have things like direct deposit and bill-paying in effect the first method generally keeps things going. The second method can create havoc for you.
Jack