Pull the breaker out that runs to the garage now, take to Hardware store of choice, tell them you need that style for 220. Basically it'll be a double of the 110. There are a bunch of different styles. I've always found it easier to take the old one with me and match it up. There is probably a style name for each but I've never bothered to find out. Match the wiring that you get to the maximum amps pulled. Get a roll of wire, fasteners, plug of choice.
If you are gonna be going back and forth between the two I would make them so they can plug in to a single outlet. Like a Stove or Dryer. Mount it on the wall. At that point wire Compressor and Welder to math the socket on the wall, and you're all set.