Unless you are having a pulsation problem or overheating your compressor, you won't accomplish much. The tank pressure is only going to be as high as the pressure of the compressor, which is probably around 20 to 30 psi. It will act as a reservoir for the air at the max pressure of the compressor, but unless you get a HUGE tank you'll only get a few minutes of painting before it drops below the required pressure.
If you want to do it, what you will need is:
1) A pressure line from your compressor to the tank. I'd use some sort of quick-disconnect fittings so you can disconnect it easily. 1/4" NPT threads are the most common, so if your compressor already has an outlet that size you won't need any sort of adapter.
2) A Check valve in the line from the compressor to the tank so air can only flow one way (compressor to tank).
3) An outlet on the tank for your airbrush. This needs to be a self-closing fitting so that if you unplug your airbrush you won't loose all your air.
4) A drain cock on the tank. As air is compressed moisture is going to get squeezed out and collect in the tank. You need to be able to drain this regularly.
5) Optionally, a pressure switch. This will turn on the compressor when the tank pressure falls below a preset level.