Instructions
Touch the "Go Out" option while you are at home with your dog, then select "Walk." Pick the dog you want to take for a walk, if you have multiple dogs.
Use the Nintendo DS stylus to draw the walking route for you and your dog. On the route map, look for any blue "?" symbols. If you see any, draw your route so that it crosses over them. You are then taken outside to walk the dog.
Wait for the dog to reach one of the "?" symbols on the map. The dog runs off, and may randomly come back with the fireman's hat as a present for you.