One thing that has not been touched on is that one cannot merely ride more hills, or even more miles to improve performance. If you're constantly riding too high a gear (running a cadence down in the 60's to 70's) or your bike is not set up well for your body dimensions there will be a definite limit on how much you can change performance. Also, when tackling a climb that ends more steeply it's important to not attack the first part of the climb. You can't get a head start on a long hill.

Note: I will agree that pushing higher gears can have a role in getting better on hills, but I don't think that works very well if one is not in shape in the first place.