The mouse is fully autonomous. At the start, the mouse only knows that the coordinates of the goal and that the goal is some combination of to the right and front of the start square.

Currently mice use reflective infrared sensors. The reflected infrared light is used to estimate the distance. Based on this reading, one can determine the position of the mouse and the presence/absence of the wall. This information is used to create a maze map and to navigate.

The Circuit Cellar article mentioned in this thread is an awesome comprehensive introduction to micromouse.