It's very common for an old Sturmey Archer AW hub to go out of adjustment. It's also really easy to sort it.
 
Put the gear lever into second (normal if you have a really old one), Turn the adjuster, labled X4 in the picture above until the shoulder of the indicator rod is level with the end of the axle. The indicator rod is the thing the chain is attached to. Then turn the locknut (K227) so that it is tight up against the adjuster and holds it in place.
 
Turn the pedals backwards a bit, then change into first, then third, then back to second. Have a look to see if the shoulder of the indicator rod is still in the right place. If it is, good, if not, repeat the process.
 
If after this the gears still don't work you will need to bring it in. There are a number of other adjustments that can be made.
 
Check the tightness of any clamps or cable stops that guide the cable along the frame. These can come loose and lead to gear adjustment problems.
 
If it makes a grinding noise, then it probably has some interesting broken bit inside. If it is an AW we can fix it fairly cheaply.
 
DO NOT TAKE A HUB GEAR APART WITHOUT THE INSTRUCTIONS TO HAND.