If it is a Swiss tournament, the next round should start automatically when all the games of that round has finished. (Therefore there cannot be a set time when the next round starts as it is dependent on when all the games finish, which could take different amounts of time). If it an Arena tournament, you have to manually start each game.
In the upper right corner of your screen, you should see several tabs. When you finish a game, you should see that you are in a tab named Play. Next to that tab should be a tab with the name of the tournament. To exit the finished game screen, just close the Play tab and you'll be sent back to the tournament tab, where you can see all the info about the tournament, including all the games that are remaining and your standing.
Sorry if that was a bit much, here's a helpful article about tournaments on Chess.com:
https://support.chess.com/article/621-how-do-live-tournaments-work-where-can-i-join-one
Joined tournament for first time today, played one game, and don't know what happens next. Does another opponent come along automatically or have I got to do something to start Round 2?
I was expecting, when a match was over, that I'd be sent back to the leaderboard or get a notificn that the next round is round x and it starts in y mins. Or something. But I just get stuck on the screen at the end of my last game.
What am I missing?