chess leagues on 20th
It's pretty well explained in the News article:
https://www.chess.com/news/view/chesscom-releases-leagues
You play rated games, in events or random challenges, and you get trophies for wins and draws. If you finish the week in a high enough place for your league tier, you move up to the next league after your first game of the next week.
If you need help, please contact our Help and Support team.