A garage is an ideal place to store your riding mower. The inside remains dry and experiences few temperature fluctuations during the day. Garages have the benefit of already being constructed and therefore not taking up additional space on your property. However, putting your lawn mower in the garage will take space away from storing vehicles and is only an option if the garage is large.
A shed can keep your riding mower out of the elements. Custom sheds are available for riding mowers or you can build your own. If built properly, a shed will stay almost as dry as a garage, but poor construction will leave you with a shed that leaks. A shed will take up additional space in your yard and can be an eyesore if not maintained.
The dealer who sold you your riding mower also has a variety of covers available for the mower. A cover designed for your specific model of mower will fit best. However, if you have an older model of mower or can't afford a custom cover, a large tarp will suffice. The tarp needs to fully cover the mower. To keep moisture out, don't allow the tarp to drape on the ground. Secure the tarp to the wheels of your mower to keep it from blowing off.
Before putting your mower away for the winter, you need to drain the fuel to reduce the possibility of fires and to keep the fuel from going bad in your tank. Remove the mower's spark plugs and then drain the fuel into a gas can. Hook the spark plug up again and turn on the mower. Let engine run until it uses up any remaining fuel in the system. This is also a good time to perform any cleaning or maintenance your mower needs.