There are a couple of details I can't quite reconcile (for example, the Fed balance sheet shows initial funding of $29.3 billion, but everyone says Maiden Lane III paid $29.6 billion for the CDOs), but essentially it went like this. The banks had bought CDS protection on $62.1 billion of CDOs (some of those CDOs they owned — some they did not, meaning those were "naked" CDS*). As of November, the market value of those CDOs was $29.6 billion. At that point, the banks already held $35.0 billion in cash collateral from AIG to cover the difference. (If you have a derivatives contract with someone under which your counterparty may have to pay you a huge amount of money, you generally negotiate a term under which the counterparty has to give you money as the trade moves against him, to protect you from default. In this case, a lot of the collateral came from the $85 billion credit line the Fed gave to AIG in September — otherwise AIG would have gone bankrupt because of collateral calls.)

In the transaction (I'm working off the New York Fed summary), first AIG contributed $5 billion to Maiden Lane III and the New York Fed gave it a $24.3 billion loan. Then Maiden Lane III gave all $26.8 billion to the banks in exchange for the CDOs. (The banks accepted $26.8 billion because  they already held $35.0 billion in collateral; together that makes $61.8 billion — as I said, I can't get $300 million to reconcile.) Then Maiden Lane III gave $2.5 billion right back to AIG (this is the amount by which AIG had overcollateralized). As part of the deal, the banks agreed to tear up the original CDS on the CDOs, so AIG couldn't lose any more on the CDS (which, remember, are separate from the CDOs).

The controversy is not over paying $29.3 (or $29.6) billion for the CDOs, since that was the market price. The controversy is over whether AIG should have agreed to settle the CDS at 100 cents on the dollar (meaning that the banks get the difference between the face value of the CDOs and their current market value).