The actual games of Touhou are classified as danmaku--what this described as is essentially curtain fire. A very fitting name, indeed, as enemy attacks come in the form of a wide assortment of colours, sizes, and shapes and in huge quantities. These attacks are also sent your way in intricate patterns, requiring both amazing concentration and memorization. To progress, you avoid these attacks by moving either regularly, or "focused" (moving much slower and being able to see your hitbox), whilst shooting off your own attacks. In a pinch, you can even set off a spell card, which grants you temporary invulnerability and causes massive damage to the enemy. Grazing, an action where you get close to the enemy attacks but don't actually get hit, is also a part of gameplay that gets the player extra points and is encouraged--when possible without hugely risking one's chances of winning.

A few spin-offs of the danmaku games have a appeared, in the form of fighting games and two photography games. The fighters are played as typical fighting games are, with much button mashing, however there is (of course) more of a focus on projectile attacks for most characters. As for the photography games, it's essentially danmaku, but instead of shooting off your own attacks, you shot photographs of the patterns being sent at you.

And trust me, playing these games a lot will improve your hand-eye coordination. By many times.