Pressure is adjusted at the controller between the airbrush and the air source. A single action brush allows only the control of air at the trigger, (on or off.) Amount of paint is adjusted at the airbrush flow controller.
A double action allows the flow of air by the same way as a single action, (pressing down on the trigger,) but additionally modulates the amount of paint allowed to flow by pulling back on the trigger, (pulling back less = less paint, pulling back more = more paint.) Simply stated, double action means trigger down for air, then back for paint.
I enthusiastically recommend starting with a simple single action, it might well be all you will really need anyway. If you need more control you can always move on to the next type, but a single action is a cost effective way to get started. Look for deals at the reputable dealers like TCP and Chicago Airbrush. I've made some great buys through them over the years.
Good luck with the search, and I heartily recommend a thorough look at Don Wheeler's site, as mentioned above, Snib's as well. A wealth of information is a quick click away, I have used it often through the years and learned much that helped me greatly.
Patrick