Ideally, you would store your kayak indoors. A garage or shed are the best options for storing your kayak, supported in at least two places. Kayaks can be stored on the wall held by hooks, hung from the rafters, or on end as long as the nose is supported and padded. If stored outdoors, you will want to make sure all hatches and the cockpit are covered, and that it isn’t somewhere that will gather snow or ice. Cover for protection, but with air flow so the covering doesn’t bake to the surface of the kayak in the sun, or allow mold and mildew to gather.
You should always clean your kayak well before storing it for the winter. Remove any debris that may have gathered, wash down the kayak inside and out with soapy water (dish soap like Dawn works fine), rinse, and let dry. You may apply wax or other marine products to protect your finish from oxidation; this should be done 1-2 times a year anyway, depending on the amount of use.