If you are on the Android app, you just need to go to the Tournaments menu item. That will allow you to connect to the Live tourneys. There is also a Daily tab there which launches an embedded browser taking you to the v2 webpage for those.
On iOS, Live tourneys are not currently available, but are in progress last I read. There is still a Tournaments option, I think, if it is anything like the older Android app. Just go to Play and click the +. Then choose the Tournaments link, which will take you to the embedded page for the Daily/Correspondence tourneys.
One other option, that I have heard works, but isn't officially supported, is to join Live in the browser, join a tourney and then bring up the app and go into Live. As long as you are logged into live, and not playing another game (I guess) you will get paired as soon as the first round starts. It may or may not work very well, so use with that caveat.
How can we join tournaments from the chess.com app?