A CLA (clean, lube & adjust)...I'm thinking that it will depend on where you are and where you can take it. Just as a random guess...I'd say it could be anywhere from $50 to $150. The AE-1 is a good camera and should work well, if in good shape...but you could probably buy two or three of them for $150.
Mike's range sounds about right. I've paid as little as $75 to as much as $190. If your camera doesn't need much extra beyond a good cleaning (ie, the seals don't need replacing, and there are no known other problems with the camera) is should be on the lower side.
Still, it's a worthy investment to get it done right. Should perform beautifully for years once it's back up to par.