The impeachment process is a two-step procedure. The House of Representatives must first pass by a simple majority articles of impeachment, which constitute the formal allegation or allegations. Upon their passage, the defendant has been "impeached". Next, the Senate tries the accused. In the case of the impeachment of a president, the Chief Justice of the United States presides over the proceedings. For the impeachment of any other official, the Constitution is silent on who shall preside, suggesting that this role falls to the Senate's usual presiding officer. This may include the impeachment of the vice president, although legal theories suggest that allowing a defendant to be the judge in his own case would be a blatant conflict of interest. If the Vice President did not preside over an impeachment (of anyone besides the President), the duties would fall to the President pro tempore of the Senate.
To convict the accused, a two-thirds majority of the senators present is required. Conviction automatically removes the defendant from office. Following conviction, the Senate may vote to further punish the individual by barring him from holding future federal office, elected or appointed. Conviction by the Senate does not bar criminal prosecution. Even after an accused has left office, it is possible to impeach to disqualify the person from future office or from certain emoluments of his prior office (such as a pension). If there is no charge for which a two-thirds majority of the senators present vote "guilty", the defendant is acquitted and no punishment is imposed.
I also think we should elect Federal Judges and have term-limits on them.