When cycling on flat stretches most of the resistance comes from your drag coefficient (aerodynamics), while at lower speeds climbing the limiter is weight. In either case the more power (watts) you can develop the better, and I'll assume you're at a competitive body weight. So the only factors you can alter to help your climbing are form, gearing choices, and your confidence.

Climbing form should be slightly different than body position on the flats since overcoming wind resistance is less important. On climbs you should sit up straighter with a hand position higher on the bars. The higher position will make it easier to breathe and put less stress on your lower back. A change in position is a good thing as it uses muscles in a slightly different way and gives some relief.

Optimal gear choice is crucial to climbing efficiently. On the flats I recommend choosing a gear that gives a cadence matching your run turnover, which for most of us is 85 to 95 pedal strokes per minute. On climbs your cadence should drop slightly to about 75 on average. For short, steep stand-up climbs I sometimes go as low as 65, but that's rare. There's no advantage in going to the extremes, pushing an excessively high gear, or spinning up climbs. After a bike race you're done for the day, but in a triathlon poor gear choices are magnified, leaving your legs with less energy for the run that follows.

Most modern bikes have a drive train that will shift under pressure, but it's still wise to make the front shift from large to small chainring well before you get to the steep part of a climb. Also, before a race where you expect to use your lowest gear (inside cog in the back), check to be sure your gears are adjusted properly. A bike can fall over just once on the right side and bend the rear derailleur in just slightly. Then you make the shift to lowest gear and the derailleur goes too far, beyond the inside cog and into your spokes—not a good thing!

Body position should be relaxed and powerful on climbs. Most riders move their upper body more as the get closer to max output, but too much motion uses energy better saved for the legs. As It's OK to sit up straighter for climbs, and sometimes this requires a unique hand position on bikes with bullhorn style bars. On my tri/TT bike I hold my aerobars just beyond arm rests with a narrow hand position. Hold the brake levers or tops of bars on a road bike with drop style bars.

For some riders it's easier to focus on using all the available leg muscles at lower cadence on climbs (though you should be pedaling like this all the time). Push forward with your quad muscle over the top; pull back with your hamstring at the bottom; pull up with your hip flexor as your leg moves back to the top.

A decision to make on a climb is whether to sit or stand. Standing increases power potential with your full body weight, but is energy intensive. It's appropriate for short, steep hills that are done in 30-seconds or less to keep your momentum and speed. Getting out of the saddle also works for steep sections of long climbs like switchbacks, again, you should not stand for more than 30-seconds. Use standing on climbs to keep your momentum for short bursts.