Article I Section 3 Clauses 4, 5, 6, 7

[4] The Vice President of the United States shall be President of the Senate, but shall have no Vote, unless they be equally divided.

[5] The Senate shall choose their other Officers, and also a President pro tempore, in the absence of the Vice President, or when he shall exercise the Office of President of the United States.

[6] The Senate shall have sole Power to try all Impeachments. When sitting for the Purpose, they shall be on Oath or Affirmation. When the President of the United States is tried, the Chief Justice shall preside: And no Person shall be convicted without the Concurrence of two-thirds of the Members present.

[7] Judgement in Cases of Impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: but the Party convicted shall nevertheless be liable and subject to Indictment, Trial Judgment and punishment, according to Law.

This is a big one, sets out what role the VP will have in the senate (a tie breaker role), when the VP is not around the President pro tempore (meaning literally “for the time being”) runs the joint. The President pro tempore also is in line to become president if something were to happen to the President and VP. Modern custom dictates that the President pro tempore will be the senior member of the majority party.

The House votes to impeach someone, its the Senates job to convict them (or not to convict them). If the President is the one put on trial the Chief Justice runs the show. This is because the VP has too much to gain and could be tempted to axe the President just so she/he could get the job.

A two thirds majority is required to (67 if all 100 senators are present) remove someone from office. When Clinton was on trial, two votes were held one of 55 not guilty 45 guilty, and one of 50 not guilty and 50 guilty. Nowhere near what is needed to remove him from office. As such successful impeachments tend to be political in nature. If one party is in control of the house and senate it is unlikely that any of there party members will be impeached or removed from office (even if like GW they seem to have broken many laws).

Those convicted by the Senate are removed from office, and can be barred from holding further office. The Congress can’t do anything else to them, but they are still able to be prosecuted criminally or sued, just like any other citizen.