From the Main Menu, swipe to the side until you see an Open Tournament. Tap on the Open Tournament. If you're currently in an adventure, tapping the green arrow at the top left of the screen (the back button) will take you to the Main Menu.
Once in the tournament, you will be given a choice of three opponents. Tapping one will allow you to see their team in more detail before choosing to fight them by tapping "Start". If you'd rather fight a different team, you can tap the red skip button at the bottom of the screen.
Both skipping an opponent and fighting an opponent cost stamina.
You can return to the selection screen by tapping on the green arrow at the top-left of the screen.