I know there has been talk already about whether or not a former president can be impeached. I have not, however, heard the practical ending to that talk. What happens with Trump's second impeachment (over the events of Jan 6 2021) now that he has left office (or will have left office come noon time)? Are there practical answers? All I've heard is theoretical discussion - but it is not a theoretical issue anymore.
The normal impeachment procedure still applies. The Senate will hold a trial after the House sends the articles of impeachment over to the Senate. At the moment, it appears the articles will be sent to the Senate at the end of this week, with the trial being carried out the following week. From ABC News:
House Speaker Nancy Pelosi is expected to send the article of impeachment against President Donald Trump to the Senate later this week, sources familiar with the matter tell ABC News -- a move that could kick off formal proceedings the next day and opening arguments on the Senate floor the following week.
The timing of formal transmission from the House to the Senate is significant, as the Constitution dictates that the trial begins at 1 p.m. the following day.
Specifics such as whether witnesses will be called are still being decided.
Also, it's worth noting that the vote to bar an individual from holding public office again comes after the vote to convict. As such, even if the vote to convict and remove a President is moot, the subsequent vote to bar the individual from holding public office again is not moot. See If the senate cannot remove a federal official already out of office, how can they disqualify said person from running for office again?.