Badger has two hoses, a vinyl one and a braided one. The vinyl hose has 1/8" connectors on both ends. The braided hose has a 1/8" conncetor on one end (for the airbrush) and a 1/4" NPT connector on the other end. If you got a braided hose and the compressor has 1/4" NPT threads you should be fine, if not you may need an adapter to go from the compressor to 1/4" NPT. If you got the vinyl hose you'll need to get a Badger adapter to go from 1/8" to 1/4" NPT.
I'd also recommend you get a roll of Teflon tape. You can get it in the plumbing department of any decent hardware store. Put a layer of tape over the connections when you screw them together and it will make them air tight.