Once your Hero's ability has completed charging up, you can tap on the ability's icon to use it. Hero abilities charge up gradually over time and can be sped up by inflicting damage on the opponents. The more damage you do, the faster the skills charges up.

Please note, you have to first unlock the ability before you're able to use it. You can unlock Hero abilities by promoting your Heroes. To view what skills are available and when, tap on the "Heroes" button at the bottom right corner, select a Hero, and select "skills" on the bottom right corner. 

Some abilities are passive, and will trigger during certain conditions, or will always be active.