If you take good care of your Craftsman riding lawn mower, it will service you for years. And over those years, you will inevitably have to replace some its parts. Normal wear and tear (and the occasional accident) will lay claim to certain parts of your mower over the years. However, if your mower is relatively new, check your warranty before you purchase new parts. Replacement parts may come courtesy of the manufacturer.
Refer to your owner's manual. This will not only include your warranty, but also specific order numbers for certain parts of your riding mower. Knowing these numbers will make ordering and finding these parts much easier.
Search the Craftsman Web site (see Resources). This is the best place to find replacements for parts that need to be periodically replaced like blades and trimmer lines for specific models. However, you will not be able to find replacements for less-common replacement items like broken parts.
Search online. Many major third-party craftsman dealers like Sears, Home Depot and Outdoor Distributors keep a wide variety of Craftsman riding lawn mower parts.
Search the classifieds. Not many retailers will carry replacement parts for a riding mower model that has been discontinued or is no longer popular. The best way to search for these parts is through online classifieds like Craigslist. You may find someone who is selling a broken lawn mower that is the same model as yours. Or, you can create a post advertising the parts or the model of lawn mower that you are looking for. The response may not be immediate, but for older models this (and junkyards) will be your best bet.