In order to understand this you have to understand that in American corporations are persons. When Mitt Romney said, "Corporations are people too" at the Iowa State Fair he wasn't sharing his own personal beliefs. Instead he was telling the truth. See Corporate Personhood[1] for more.

From this it follows that Corporations have the right to free speech. This is where the supreme court ruled[2] that it is unconstitutional to deny corporations the right to political speech.

The legal requirements are disclosures and that's why you hear "paid for by Americans for a better tomorrow" or something like that. Corporations don't directly give to campaign coffers, but through a series of transactions often via PACs (political action committees) it eventually gets to where it's going. It is illegal for PAC's to coordinate with the campaign, but this does happen in subtle and less than subtle ways.

[1]http://en.wikipedia.org/wiki/Corporate_personhood [2]http://en.wikipedia.org/wiki/Citizens_United_v._Federal_Elec...