With a single action... the paint flow is either on or off... you adjust the amount of paint flow with a small knob.
With a double action, you start and stop the airflow just as witht the single... but you control the amount of paint flow by moving the same trigger button foward and back.
So you get more control as you move around wha tyou are painting, without having to manually adjust the paint flow.
Once you get used to it... the double action gives you a lot more control.
For your first air-brush... I would recomment an inexpentive single action. This will give you time to get the other things worked out... like how; how much to thin the paint; how to move the air-brush etc.
Then when you feel comfortable, and feel like you need more control, move on to the double action.
You can then stil use your single action for priming, and coating etc.
Here is my Air-Brush section:
http://www.naplak.com/modeling/tips/air-brushing.htm
www.naplak.com/modeling ... a free site for modelers
www.scalehobby.com/forum/index.php ... a nice Modeling Forum