It's like Young Witch but with only one card instead of a kingdom pile of 10 cards. You pick a 2-3 cost action card that you are not using in your kingdom setup, and you set aside 1 copy of that card.
Official FAQ:
Set aside any unused Action kingdom card costing $2 or $3 at the start of the game. Do any setup that that card requires.
When using Way of the Mouse, you play the set-aside card, leaving it set-aside. For example, if you set aside Sleigh, then any Action card could be used to gain 2 Horses.
The set-aside card cannot move itself when played, since it is not in play; for example, if the card is Embargo, it cannot be trashed.
Text below a dividing line (other than setup) will not do anything.
Other rules clarifications:
If the set-aside card is a Duration, then a card played this Way will stay out as long as that Duration would.
You cannot use Way of the Mouse when playing the card set aside by Way of the Mouse, to prevent loops that could matter with Champion.