If the event is a tournament or other match-playing event make sure every one has finished their games and all scores have been entered. For a knock out competition you'll want to verify that the finalists are correctly in place in the draw(s).
Next, move the event into the completed stage. You do this by identifying the event in Manage events and clicking on the Progress to next stage button (assuming it's in In play stage). Be aware that if this event attracted a nominal fee then payment on account will be taken from all joiners when this happens. If the previous event was still in the completed stage then you'll have to move this into the archived stage first.
If you want, you could write up a report on the event for posterity by selecting the Report tab in Manage events.