The original idea was to buy up "toxic" debt that Wall Street firms have on their books (those mortgage backed securities mentioned above), but the Fed later shifted gears and thought it wiser to directly buy stock in faltering financial institutions. (NYT, WP) Plan B then became Plan C when the Treasury rescued CitiGroup and combined both models, buying $20b in Citi stock while "backing" $306b in bad assets (those assets will stay on Citi's ledger, but the government will pay for any steep losses they incur) (NYT).
As part of the bail out package, the government is supposed to get some stock in the companies they help out (which means taxpayers could - in theory - end up making a profit if/when firms recover).
CEO pay - and golden parachutes - in those companies were originally also supposed to be limited (although in an unenforcable way - WP); Congress later tightened the screws on exec pay in bailed-out banks (WP), but Obama may try to loosen them back (NYT). (NYT, WP) Meanwhile, a flak over excessive bonuses at AIG boiled over into an attempt to retroactively tax AIG bonuses - but eventually simmered down (WP). As of June 2009, a "compensation tsar" was hired to set rules on executive pay at bailed-out firms (WP).
As of the end of '08, the Treasury had already used up its first $350 billion of the bailout, meaning it had to ask Congress for the second half. Although Congress had the option of holding back the cash - and some lawmakers wanted to attach conditions to releasing the funds, including more transparency and a guarantee that some of the funds will go to help homeowners running into foreclosure (WP) - the Senate effectively handed over the second $350 billion in January (NYT).
See also Slate's interactive Bailout Guide and the New York Times' ledger of where the $700 billion has gone.