Hi D_LaMz, that is basically the same as my comp, remove the hose from this fitting:

if your Badger airbrush airhose has a 1/4 bsp fitting on the end it will screw straight on, if it hasn't you can buy a fitting which will take the small Badger fitting upto a 1/4 bsp, try your local hobby shop, they should be able to help you out, if you want a water trap get something like this from a place that sells comp spares:

you'll need a fitting like this to go in the output side of the filter:

just connect up your hose to the fitting and away you go, oh, nearly forgot, get some "PTFE" tape as well to make nice air tight joints.
Let me know how you get on and if this has helped you.