Consult the original manual for your travel trailer and decide whether to stick to replacing parts with items from the original company and era, with new parts following the original aesthetic or with new parts that you can easily find. This decision will affect the cost and duration of your project as well as the look of the trailer.
Inspect the trailer for serious as well as small defects such as holes in the walls or roof, leaking windows, rotting wood, rusted metal and missing parts. Notice if there are any additions that are not original to the vintage trailer as you may decide to remove them to maintain style.
Turn on all the lights and the heater, open the windows, check the brakes and try all the locks to verify the systems are operating appropriately. These systems can be troubleshooted by consulting the manual, but if significant repairs are required, consult an expert to avoid damaging the trailer or hurting yourself. Smaller trailers often have water systems or bathrooms to check.
Clean the interior by wiping down all surfaces with warm water and dish soap to remove dirt and grime and removing molding or worn out fabrics. Remove unwanted additions and parts you wish you replace such as door handles, windows and cushions.
Repair damages by filling holes in the wall with drywall mud, replacing rotting wood, treating rusted metal with Rustoleum or other treatment and replacing window treatments and cushions, if removed. Consider replacing the tires if they are old or worn. This step is where you will need to hunt down original door handles, windows and other accessories if you decide to use original parts. You can find new parts in RV and hardware stores.
Seal the trailer by treating the roof with sealant and caulking the exterior of the windows and doors to ensure proper heating and cooling. You may also want to consider a new paint job.