Hey Lord Raffickus, welcome to the Forums.
Whenever you initiate battle with your army, you automatically compete in the weekly Tower Tournaments.
You do need to have the Tower unlocked in your Map, or you will not be awarded possible Victory Medals.
At which Tower you compete depends on the units in your army. The highest Age unit in your army determines which Tower you compete at, despite any number of other units in your army.
Tournaments start around Monday afternoon and end on Sunday afternoon. (CET)
Hope that helps!
- L