Since this is a power of Congress, you need to be looking in Article I, rather than Article II. (That said, I would have thought it was about the President, too :))
The relevant pieces of the document are:
- The House has the power to bring articles of Impeachment (i.e. start the proceedings)
The House of Representatives shall chuse (sic) their Speaker and other Officers; and shall have the sole Power of Impeachment.
- The Senate actually conducts the trial, and must vote guilty by at least a two thirds margin.
Article I, Section 4:
The Senate shall have the sole Power to try all Impeachments. When sitting for that 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.
Judgment 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.
Beyond these rules which are set in stone by the Constitution, anything else would be subject the rules of the House and the rules of the Senate - basically the rules that are the parliamentary procedures of each body. Reference to committees, for example, falls within these rules. These rules are adopted at the beginning of each session, and define both the makeup and purpose of each committee. Committees (and any rules associated with them) are just a thing to make the body function better - if the body agreed to suspend the rules, for example, each body could set up any procedure it wanted, subject to the Constitutional limitations proscribed above. To cite a silly example, if the Senate decided that the impeached president had to attend the proceedings whilst wearing a pink tutu, the Supreme Court could not intervene on these grounds. (Cruel and unusual punishment perhaps, but the point is that within each chamber, each body can do whatever it wants.)
Historically, the House has brought articles of impeachment against a president four times.
- Andrew Johnson was impeached, but the Senate failed to convict by 1 vote.
- Bill Clinton was impeached, but the Senate failed to even to muster a majority.
- Donald Trump was impeached twice, but again the Senate failed to even muster a majority.
It should also be noted that the House was about to bring articles of impeachment against Richard Nixon, but Nixon resigned first.