You can view and join tourneys by going to the Play option and clicking the plus-sign like you are going to start a new game.
There, choose the Tournaments option. That will take you to the site where you can browse what is available. You don't see a list of upcoming Live tourneys there but when I just checked I can see the next one and there is a button to Join. I believe that will sign you up and games will launch on the app when it starts .... though I have never actually tried it.
how do i participate in a Tournament. I am not able to see any option to join a Tournament from Chess.com mobile app.