Airbrushing with a CO2 tank
First, why would one want to use a carbon dioxide tank with an airbrush pistol? There are two common sources of compressed "air" (any kind of gas really) for airbrush: Compressed air cans or compressors. Cans don't last very long, are often filled with flammable gas (butane/propane), and get very cold when in use (gas cools down when it expands.) Compressors are expensive, heavy, can be loud, and need a water trap to prevent water from getting into the airbrush pistol (again, gas cools down when it expands, causing the moisture in the compressed air to condense.)
Carbon dioxide tanks, on the other hand, contain a lot of gas (the smallest ones are 1.5kg, normal "portable" size is 7.5kg, and you can get up to 30kg in one tank), the gas is not flammable, it's naturally dry so doesn't need a water trap, and is comparatively cheap to refill. CO2 tanks don't cool down as much as compressed air cans because they have a lot more mass. Plus, if you own a fish tank, you probably have one of these already.
This is what you need, and where to get it (prices and sources reflect my experiences in Switzerland; you might be cheaper or find different sources.)
A carbon dioxide tank: You can get these either from a pet store (for use with fish tanks), or from a specialist gas supplier (like PanGas in Switzerland.) If you don't know where to get one, ask at your local hardware store -- carbon dioxide is used for welding, and if the hardware store sells welding supplies, they know where to get the gas for welding. These tanks work either on a deposit system or a rental system; I paid 100CHF deposit for my 1.5kg tank from the pet store, but I could also rent one for 60CHF a year. Refills are about 40CHF and get dramatically cheaper with larger tanks (a refill for a 1.5kg tank is the same as a refill for a 7.5kg tank, for example.)
A pressure reducer: Carbon dioxide tanks have between 50 and 70bar (1000psi) of pressure. You need a pressure reducer to get this down to a safe pressure of 1-2 bar for your airbrush pistol. A pressure reducer is about 80CHF at a good hardware store or DIY store. Be sure to get one for Argon/CO2 -- every type of gas has a special kind of thread on the tank (for CO2 it's something called "W 21.8 x 14TPI") to make sure you don't connect the wrong equipment to a tank. A pressure reducer for a different kind of gas won't fit. Be aware that there are two kinds of pressure reducers for welding: Constant flow and constant pressure. You want a constant pressure reducer -- these are the ones with two dials. (Constant flow reducers have one dial and a strange glass vial that shows how much gas is flowing.)
A reducer for your airbrush pistol: The pressure reducer's output has a 1/4" thread, and you will need a reducer to attach your airbrush pistol. Airbrush manufacturers tend to use custom non-standard thread sizes, so get one from your airbrush manufacturer.
That's all you need, and it should set you back 200CHF or less. To connect it up, first connect the pressure reducer to the gas tank. It is good practice to blow out the valve of the gas tank first (open the valve a tiny bit until you hear gas rushing out) to remove dirt that might otherwise end up in the pressure reducer. Close the main valve again and screw on the pressure reducer. Then connect the reducer to the pressure reducer; you may need teflon tape (and potentially lots of it) to achieve a tight seal. Connect the airbrush, and you're set.
The pressure reducer will come with a manual on how to connect it and how to operate the valves. Always read the manual carefully -- you are dealing with 70bar of pressure in the tank, which can do quite a bit of harm if handled improperly.
Usually there are three valves in this setup: The main valve on the gas tank, the regulating valve on the pressure reducer, and a secondary valve on the pressure reducer. Typically, you close both valves on the pressure reducer fully. Then open the valve on the gas tank. Use the regulating valve to set your desired output pressure (typically 1-2 bar for airbrush), and open the secondary valve on the pressure reducer to allow gas to flow to the airbrush piston. Now you're ready to start airbrushing.
To disconnect the pressure reducer, first close all valves (both valves on the pressure reducer, and the main valve on the tank.) Trigger your airbrush gun to remove pressure from the hose. Disconnect it from the pressure reducer. Then first open the secondary valve, then the regulating valve, to remove pressure from the reducer. Now you can disconnect it safely. Close the valves again before storing it.
I hope this explanation helps some people. Please leave comments if you have any questions.
Here are a couple of pictures of my setup: