How fast is an impeachment procedure?

It took over a year both times for Nixon and Clinton.

Not fast enough

"Impeachment" means that your fitness for a job, or your truthfulness, has been called into question. It is the first step in the process to remove a government official from office. In the case of the President, it is done by a simple majority vote in the House of Representatives. That can occur pretty quickly. In Andrew Johnson's case, it was three days from the time he violated the Tenure of Office Act, to the House's vote to impeach. In Nixon's case, impeachment started on February 6th (although the effort that led to his impeachment started almost a year earlier with the Senate's creation of an investigative committee), and he resigned rather than be impeached on August 9th. In Bill Clinton's case, efforts toward impeachment began on or about January 17th when the media picked up the story of his sexual encounters, and culminated in an impeachment on December 19th.

That doesn't remove the President from office, though. There has to be a trial first. The trial is conducted by the Senate, with the Chief Justice of the Supreme Court presiding. The Senators are a 100-person jury. The trial can take longer, or be quicker, than the impeachment. In Johnson's case, it went from March 13th to May 26th. In Clinton's case, it went from January 7th to February 12th.

Not very. The House has to debate and vote on a bill of impeachment, which is followed by a trial in the Senate.