Double check the adjustment in all gears. In low gear, you should be able to see that the sprocket moves faster than the wheel, and the hub should not make a ticking sound while being pedaled forward. In middle gear, the sprocket should move at the same speed as the wheel, and you may hear a slow ticking as you pedal. In high gear, the wheel should turn faster than the sprocket. The same slow ticking may be audible in high gear.
If you hold the trigger halfway between middle and high gear, the hub should disengage so that you can spin the pedals forward without going anywhere. If it freewheels forward in high gear, the cable is to tight or has too much friction to release properly. If it freewheels forward in middle gear, the cable is too loose.
If you're anything like me, you will have to make many minute adjustments to the cable tension until you get it just right. The key points again: 1) properly seat indicator spindle in hub; 2) freewheel in high gear means cable is too tight; 3) freewheel in middle gear or low gear means cable is too loose; 4) there should be no ticking sound when pedaled forward in low gear; 5) hub should freewheel between 2nd and 3rd gear.
If you would like to read Sheldon Brown's original article in its entirely, go here. Sheldon also has lots of other great information about three speed (a.k.a. planetary, or epicyclic) gearing, including diagrams that show what's going on in there.
By the way, my experience related here is based on the Sturmey-Archer AW hub that is original to my Columbia, I have no experience with other S-A models or other hub-geared systems.