If the Americans guarding the embassy taken over panicked when the protestors broken in and opened fire they might also be put on trial and then either imprisoned or shot by the Iranians upon being found guilty. If this happens, the US bombs destroying the Iranian navy, air and land defenses until the release of the hostages is secured. After being attacked the Iranian people stand behind their new government and fight until a US invasion or rescue force tries to liberate the hostages.
I don't think NATO would get involved in an invasion because it's an American affair, but Saddam might because he wishes to take advantage of the situation and secure Iranian ports for himself. The Americans would win an air and sea war easily, but if they decide to invade the occupation will be long and hard and they will ultimately be forced to withdrawal in humiliation. There would be some sort of ceasefire after all of Iran's military infrastructure is destroyed and US demands for the Ayatollah and his government to leave Iran are met.
I doubt the Ayatollah leaves and Iran has to recover from this invasion. Iraq takes advantage of the situation and becomes a significant regional military power. If the Americans win a pure air and sea war there will be renewed confidence in their military and President. If they enter into a ground war it will be something like Vietnam syndrome all over again and the US doesn't interfere in foreign conflicts as much anymore.
I double they fight in the Gulf War or do too much around the world as a result. A ground occupation would bet between the size of Vietnam and Iraq and not popular with the American people.