Press the action button (Space-Bar, Enter, or "A" button on Wii U) to punch. If you hit someone they will be knocked up and away.

I also created a battle arena (door near the upper right on the "cloud" platform). In there you can't place any blocks, but you can double-jump. If you fall off the bottom, you die and after 3 deaths you get kicked out of the arena.

When you are hit in the arena your damage increases making it harder to stay on the platforms. When you die (fall off the bottom) your damage is reset.

I added a shortcut to the arena by going down the chimney (makes perfect sense, huh?)