To move the mouse, you can use WASD, HJKL, the arrow keys or the onscreen controls. As the scientist says, "use WASD, HJKL or the arrow keys to move the mouse and reach the cheese". You can only move through barriers when they turn to face you. When dealing with buttons, keep in mind that you can only activate them by moving onto them, and it is impossible to avoid doing so. There are other game elements that you need to worry about, but the game will introduce them to you when they are first used.
The levels are not timed, so play slowly when you need to. You can't make a level impossible to solve by doing something stupid, although feeding yourself to a cat or jumping in a hole may be the only solution under certain circumstances. If something kills you, you will be sent back to the beginning of the level. Just try again and don't make the same mistake.
At the end of each level you will see a code at the bottom of the game window. You can use this code to jump between levels whenever you want. To use the code, either press the Resume button on the main menu or hit the Q key during the game. Users subscribed to email notifications will also be given level codes automatically whenever a new level is released.