The President would first be impeached by the House and, if upheld by the Senate, would be removed from office. The Vice President would become President, and the impeached President would become a common citizen again. Following that, the former President would be given an actual criminal trial and convicted. He would in theory not be tried before the trial (this was a major source of trouble prior to the Clinton Impeachment).
In theory, the President has Sovereign immunity, so while he is President, he cannot be charged with a crime. Impeachment, while it's supposed to be granted for "High Crimes and Misdemeanors" has historically occurred for "any reason that gets Congress mad enough to demand your removal from office". The Supreme Court has also said that Impeachment is entirely political and thus not up for review by the Judicial branch of government (also, Impeaching a Federal Judge is more common then an executive officer. 15 of the 19 people impeached by U.S. Congress held a Judicial office (Two Presidents, one Cabinet Member and One Senator were impeached. In fact, the Judiciary is the only branch that has lost office holders as a direct result of Impeachment found Guilty by the Senate).
While never impeached, Nixon resigned before his articles of Impeachment were voted on the House Floor. Upon his resignation, Nixon was given a Presidential Pardon by President Gerald Ford, an act which was very unpopular at the time, but is today viewed by some as an act of healing the nation (keep in mind, Nixon won all but Massachusetts in the last election so his ousting was deeply hurtful to the nation. A trial against Nixon would have only made the wounds deeper.).