Alright, here's how you steal money from a bank's computer:
Make a wire or ACH transfer to another bank. Withdraw that money from the other bank. If you're of the go big or go home mentality, run that money to a lot of other banks. Taking in a big wire transfer and immediately sending it back out might look suspicious to the receiving bank if it's the only transaction, but receiving a big transfer and sending maybe 20% of it out would seem normal. Also, embedding the transfer into some other account that is normally highly active would also be helpful.
Remember, it's not yours until it's cash. Wire transfers can be reversed, so you need to make the withdrawal or get it so far gone and laundered that it isn't coming back.
Sometimes that line into the bank is through an outside computer at a regular company. This case has a few examples of where real money was taken from a bank by computer.
See the bottom of that article for links to the incidents below. The article focuses on the PATCO case which I've talked about previously
Experi-Metal Inc., which in December 2009 sued its former bank, Comerica, after losing more than $550,000 in fraudulent wire transfers;
Village View Escrow of Redondo Beach, Calif., which in March lost $465,000 to an online hack;
Choice Escrow, which in November 2010 sued its bank, BankcorpSouth, alleging inadequate security measures;
Hillary Machinery, which in January 2010 was sued by its bank, PlainsCapital Bank, after a legal battle over ACH fraud liability. The suit was later settled for undisclosed terms;
The Catholic Diocese of Des Moines, Iowa, which in August lost $600,000 in fraudulent ACH transactions.