The Tower of Trial becomes available after you purchase the Shop of Time in the Premium tab of the Shop. Note: The Premium tab does not become available until you revive for the first time.
It also updates periodically with new Rounds which will present new challenges.
Tower of trial or ToT is a crucial part of Endless Frontier. It will not be looked upon as a waste of time or gems. You need to pump as many spare gems into T3 units as possible. This goes for 2* all the way up to 5*. Dont worry though, if spent wisely, you will be able to regain these gems quite quickly. The first and in my opinion the best unit to trans 3 is skeleton warrior. It is the most diverse and gets the job done quickly and efficiently. The rewards from ToT range from a few gems at floor 1, all the way up to 400 gems at floor 35. Not only gems but honor coins as well, which makes it even more appealing.
(This is only my opinion and all I could be bothered writing, please add to this)