Towers are how you deal damage. To place them, you must first tap on a tower spot, located on each level. Every time you build a tower, the cost for the next tower will increase.
If you tap on a built tower, you will be brought to the tower upgrade menu. Here you can see some stats about the tower as well as purchase cash upgrades. Cash upgrades apply to all towers of the same type, but will be reset on a prestige. Each tower may have a different set of upgrades with a different amount applied per purchase.