If you have a compressor, or any other air source, you can buy a small filter-like unit from a variety of industrial-supply places that has desiccant in it. You pass the air through the desiccant and it removes almost all of the moisture. The desiccant can be dried out when you've used it to its limit by baking it for 45 minutes or so at 350F. McMaster-Carr, Grainger, etc. will have them.Thanks Dave, forgive my total noob question but where does an average non-race guy get "dessicated air"?
Otherwise, you can use N2 or get an air tank and fill it at a shop that has dry air.
What I do at the race track when there is no dry air available is to fill an air tank (or the tires directly) from the track's compressor using the desiccant dryer with an air chuck on it at the end of their air line.