How do I run the same tournament again?

When a series has finished, press Run it again. That sets up the next series with your settings: the size, the fee, the venue's share, the prize split and the match lengths.

Players who follow it are told straight away that it's back, before you've picked a date. So once you've set the date, let them know, for example with Bring last time's lot back (inviting players).

It doesn't copy who's keeping score, so choose that again on the day. You need a Leagology plan.