The first thing you will need if you don't already have it is a 1/4 hose with quick coupling to attach to the compressor you will find this at home depot, this one is form home depot;
After this you will need an air regulator/water filter, if you look at this photo you can see my mine with it's fittings;
This one has 1/8 holes in and out so on the left of the photo I have a 1/8 male to 1/4 female adapter piece with a male 1/4 quick connect, this will go into the your hose from home depot, on the right side of the photo I have a male 1/8 to male 1/8 which your airbrush hose will screw straight onto, you regulator should come with a bracket so you can screw it to a wall or desk, it can also be clamped to a desk, you can see my
set up here, if the regulator you end up with has 1/4 connection holes in and out you will only need the 1/4 male to male connection circled in red top, and then the 1/4 male to 1/8 male in blue oval top, it is important that your regulator has the same (or exceeds the) maximum pressure of your compressor.
I would assume you already have your airbrush hose already so once you get these parts your ready to go, although the pistol grip moisture tram and external micro air control valve are handy options, you see these just to the left of the three hoses.
Just ask if you need further assistance