Each hero has four skills. You can manually activate only the first one. To do so, press the hero icon when it starts glowing, and the energy bar is full.
The second, third, and fourth skills activate automatically according to their recharge period, i.e., cooldown time. It means you have to wait a certain amount of time before a hero can cast these skills again. You can learn the timings of skill casts by observing battles or by asking fellow players on our official communitites. Also, check out the official Hero Wars Universe website; it describes all heroes and their skills in detail.
The maximum level of the first two skills is 130, the third — 110, and the fourth — 90. Hover your mouse cursor over the name of the skill to read its description.