Something strange happened to the protagonist Ray Doewood: an alien moved into his brain! The direct effect is that Ray is now able to read the thoughts of other people. Unfortunately The Man, a mysterious villain, also has interest in the alien and sends his lackeys to capture Ray. The goal of the game is to flee from that undesirable fate.
Each level consists of a freely explorable scene in which Ray meets various humorously overdrawn people. The goal is to read their minds, find out what they desire and give it to them. Then Ray usually gets something out of it which another person desires and so on. The special gimmick is that the whole world and its inhabitants are made out of cutout paper: Ray can cut out (read: take) objects and stick it to other, predefined places in order to solve puzzles. There is also a bit of platforming involved, both in order to reach other places and to avoid The Man's men. Objects can (in some cases have to) be used in order to avoid enemies, e.g. by sticking "sleep" to a guard which desires rest.