You know, my advice is just the opposite of Jedi's. I think that most bikes do not have low enough gearing and I run 13-25 with 53-39 chain rings. In areas with long sustained climbs, I use a triple.
But a large part of that is my climbing style. I spin at a pretty high rpm whilst climbing so I tend to use pretty low gears. I was out in Wyoming on a climb and this guy with a double on his bike caught me at the beginning of the climb. He was out of the saddle at low rpm and I was sitting and using high rpm. He never did pull away.
Climbing hills better will be helped by just becoming stronger on the bike. When I started there were hills on this one road that I rode every now and then that seemed like mountains. Then I got into better shape and then they seemed almost flat.
Of course, nothing helps hill climbing better then hill climbing. Funny thing is that you really do not have to push it. I have gone out west a number of times and spend a week or two riding mountain passes. Typically, I just spin up and don't push really hard. There is nothing worse then giving out 3/4 of the way up a steep grade. But I get back here to central Florida and I can do all the hills in a gear higher then before. There is something to a couple of hours of climbing per day that really helps even if it isn't all out.