The Training Camp is a very important building in the game as it determines the maximum level of your Leaders and Preppers.

To gain access to the Training Camp, you must first complete a series of tasks from the Mayor, which appear in your main game storyline and are indicated with an orange notification on your task list. 

These tasks will unlock the camp, allowing you to locate it in your Town map (is located in the top right corner).

Once you have access, you can start leveling up your Leaders and Preppers by upgrading the Camp.