An accusation in one chamber, a trial in the other, and a two-thirds wall that has held against every President ever tried. Impeachment is the Constitution's emergency brake, built to be hard to pull.
Impeachment is the removal process for Presidents, Vice Presidents, judges, and other 'civil Officers', not a criminal proceeding, and not reserved for crimes alone. The House accuses; the Senate judges; and the penalty stops at the office door: removal, and at most disqualification. Everything else stays with the ordinary courts.
'Treason, Bribery, or other high Crimes and Misdemeanors.' The first two are defined; the third is deliberately not, the founders borrowed it from English practice to cover grave abuses of office, whether or not they are indictable crimes. In practice its meaning is decided politically, case by case, by the House and Senate themselves.
Who can be impeached: the President, VP, and 'civil Officers', judges and executive officers. Members of Congress cannot (settled in 1799); each chamber instead expels its own by two-thirds.
Impeachment begins as an inquiry, historically in the Judiciary Committee, sometimes led by other committees or a task force. Hearings, subpoenas, and depositions build the record; the committee then votes on whether to recommend articles of impeachment, the formal charges, to the full House.
The full House debates and votes each article separately; a simple majority on any article impeaches. The officer is now impeached, accused, not removed, and keeps serving. The House then appoints managers, members who will prosecute the case across the Capitol.
Source: History.House.gov, Impeachment
Senators swear a special oath to do 'impartial justice' and sit as the court. House managers prosecute; the officer's counsel defends; the Senate sets its own trial rules and votes on evidence and witnesses. When a President is on trial, the Chief Justice presides, so the Vice President never referees their own promotion.
The Supreme Court has held trial procedure is the Senate's alone to decide (Nixon v. United States, 1993, a judge's challenge, not the President's), so there is no appeal from how the Senate runs it.
Source: U.S. Senate, About Impeachment
Each article gets a separate vote, and conviction on any one requires two-thirds of senators present. That wall is the process's defining fact: it has held in every presidential trial, Andrew Johnson survived by one vote in 1868, and has been breached only for judges.
Conviction removes, full stop. A separate, simple-majority vote can add disqualification from future federal office, the Senate has done it three times. And that is the ceiling: no prison, no fine. Criminal law runs on its own track, an impeached or removed officer 'shall nevertheless be liable' to ordinary prosecution, and the President's pardon power cannot touch impeachment itself.
Stage-specific sources are cited on their stages above.