The bad news is that how you climb depends a lot on your genetics. There are people born to go up, and there are those who must earn every inch. And, it's primarily your body type that determines how you feel when the terrain gets vertical. The greater your strength-to-weight ratio, the easier it'll be to climb and the faster you'll motor up mountains and hills. That's why in major races, all the skinny people suddenly appear at the front when the terrain slopes skyward.
But don't despair if you're six-feet-four and 200 pounds. While you may never rocket up ascents like Lance Armstrong, you can definitely go up faster if you train for the hills. Mostly what's needed is lots of riding that develops power. If you want to improve your abilities on hills, start riding undulating routes regularly. You might add hill repeats (do each hill twice or pick one and go up it several times) to get the most benefit out of your rides.
It's harder to train for the ups if your main riding roads are runway flat. Here, something that's a decent substitute for hill training is heading out against a stiff headwind. Warm up and then settle into a slightly larger gear (this should slow your cadence to about 80 rpm) and push yourself as if you were grinding up a long grade. For motivation, remember the tailwind and the free ride home.
Another trick that works nicely is doing repeats on highway overpasses. Even though these sections aren't particularly steep, you can train your legs and lungs to climb if you do four or five ¾-effort repeats a couple of times a week.
It may sound silly, but something else that helps a lot of cyclists in the hills is maintaining a positive attitude. If you're looking forward to the ups, and enjoy the challenge, you'll definitely go faster regardless of your size, weight and fitness level.