Choose a gear that will allow you to spin at a minimum of 90 RPM. On a sprinter's hill where a maximum of power is required, up to 120 RPM is a better bet. Choose your pace, then exert whatever force is required to keep spinning at that rate, downshifting if you really must. Shift before you need to, both to avoid changing gears when there are huge loads on the drivetrain, and to avoid being caught in too high a gear.
If you overgear and let your cadence drop even a bit, you will end up at the bottom of a spiral of inefficiency with you out of the saddle, push-push riding the bike up at a crawl.
Choose Your Pace
On a climb that's long, the most common mistake is to choose an unsustainable pace. If you run out of gas halfway up, simply downshift and continue up at the same cadence but 15% slower. If you're already in your lowest, grit your teeth and bully your way up, maintaining your cadence to the dot. Your lowest gear is chosen so that you can do this sucessfully.
If the hill is short, it's a perfect opportunity to make up some time; hammer your way up. Your effort has the maximum opportunity to reduce your time, instead of feeding aerodynamic drag if you made the same effort on the other side of the hill. The moderately long hills are what oxygen deficits were made for! Do weight training to beef up your leg muscles, and hammer your way up, switching muscle groups as they expire. Continue the sprint over the crest of the hill with a few solid power strokes to enter the straight or descent at high speed.
If the hill is really short but steep, a good strategy is to store up energy by pedalling hard on the approach. Let your momentum boost you up the hill as you downshift and continue to pedal as you glide up.
Concentrate on breathing out.
Climbing should be a balancing act. Keep tuning the distribution of weight between you wheels; if your rear wheel loses traction, slide back, and if your front wheel lifts up or needs steering traction, lean on your arms or slide forward. Especially when climbing out of the saddle, it is all too easy to lean forward and take the weight off the rear wheel just when it needs it, resulting in spinout and bogging down -- bend at your waist when standing to avoid this. Maintain constant traction and ground contact with both wheels.
Steve Bauer, a pro racer and a Canadian silver medalist in the 1984 Olympics says on the topic of climbing technique: "You may want to stand at first to rest the muscles you were using on the flat," says Bauer. "The last thing you want to do is get into trouble early on a long climb."
Bauer suggests doing most of your work in the saddle, as you don't waste energy suspending your bady and you have a longer power cycle available. "At the bottom of the stroke, pull back with your hamstrings," he explains. "Then use your hip flexors to lift up through the top of the stroke." Resting various muscle groups by alternating between pedalling styles, such as sitting and standing, is effective only if your alternate techniques are sound. Many spin their underweighted rear wheel, put their whole bodies in the wind, and either don't bend their hips, or crunch up their chest when pedalling out of the saddle.
Bauer finds that rocking his bike helps his rhythm, in addition to the fact that it keeps your pedals at the right distance when out of the saddle. He is quick to point out, however, that "how much you rock is a very personal thing."