To deal damage, select connectted numbers counting down to 1. (For example, you could move the red to a 2, press space, then move to an adjacent 1 and press space to deal 2 damage.) If you go from 4 or higher, deal double damage. You tap Arrow Keys or WASD to move.
I would advise looking for a 1, check if there are any 2s next to it, then 3s next to the 2s, and so on, then select the highest number (by pressing space) and count down.
When the timer runs out, a new map is generated.
When you get hit, your selections are canceled.