How do I increase the slots for the units?

You will be given more room inside your tower for your units and modules every after 10 levels (of an upgrade in your tower). During the early levels of the game, you will have 3 to 4 slots for your units and 2-3 slots for modules. You will unlock all the 4 free slots (1 top, 2 center, 1 bottom) for your modules and 8 free slots for your units by the time you reach level 80. the extra for units that get unlocked when you reach level 100 will be for your turrets.