I began by removing the complete wheel assemblies from the wagon bed and disassembling the pivot plate and handle from the front bolster (the axle and support structure).
You can purchase new wheels and hub caps as well as most other parts for current wagon models at Radio Flyer's website. If you need to remove the wheels, this page on Radio Flyer's website has instructions on how to remove the hub caps. Note that they get destroyed in the process. If you're restoring an older discontinued model, finding parts may be a little more tricky . . . but there's always eBay.