The valve is in four pieces and is pretty easy to clean.
1) Unscrew the valve assembly from the airbrush body.
2) On the side that the hose screws on to notice that the hole is shaped to fit an Allen wrench. Find an Allen wrench that fits it and CAREFULLY unscrew it. There is a spring right underneath so take care not to lose it.
3) Remove the spring and plunger. Clean the valve body, the cap that screws out, and the spring with laquer thinner. Clean the plunger and o-ring with alcohol or Windex. Put a tiny amount of airbrush lubricant, Vaseline, or something similar on the o-ring and plunger. Pay particluar attention to the air holes in the side of the valve body.
4) Reassemble in reverse order (plunger into body, spring into body, and screw the cap back in place) and it should be good to go. Test it by screwing the air hose in place and pushing down on the plunger. If the compressor is on you should get air blowing out the holes in the side of the valve.
They tend to get gummed up from time to time and will occasionally stick. Cleaning them out is usually all that is necessary to get them working properly again.
If that doesn't work check the air pasage in the airbrush body. Unscrew the head and you'll see a hole bored at the 6:00 position. That hole goes all the way back to the air valve and if it gets plugged up there will be no air passing through the airbrush. You can disassemble the brush completely and coak the body in laquer thinner to get rid of any dried paint in the air passage. Blow it out with compressed air and it should work fine.