The techniques described here are intended for the very steep but the same basic principles apply when attacking more gentle gradients.
When you hit a big hill, the 'thinking thing' dials up the engine room and asks for a bit more horse power. The natural response is to stomp on the pedals resulting in spinning your back wheel like a bogan at the traffic lights. Maintaining traction demands the even application of power. So when you need a bit more grunt, turn the power on progressively and pedal smoothly. Focus on applying your power around the full circle (how Zen) instead of stomping down on each pedal. Picture your cranks rotating around a clock face (a stiff drink and an encounter with David Lynch may help create the image). The down-stroke (from 12 to 6 o'clock) is most powerful - especially when the crank is around the horizontal position. The power produced at the top and bottom of each cycle is little more than a "joke". For the moment let's assume you're not getting any power from your up-stroke either. The resultant power curve for the rotation of each pedal is vaguely parabolic. The objective is to flatten the power curve so it looks more like the dotted line. The downward power-stroke is instinctive, so focus on the 12 and 6 o'clock positions. Try sliding your foot forward at the top of the stroke while pulling backwards with your other foot (a kind-of Michael Jackson style shuffle). Also remember to pull up (against your toe clips or clipless pedals ) on the up-stroke to develop additional power.
Steep hills demand you 'get off your butt' so you can crank more power from each stroke. But you've still got to avoid power surges, which requires even greater dedication to the above principles. Practise your out-of-the-saddle technique on the flat. Tarseal is ideal as tyre noise from the road indicates changes in torque. As always, a quiet upper body helps tie the whole performance together. Avoid bobbing by concentrating on keeping your hips in the same horizontal plane.
Hill climbing is a balancing act - continually adjusting your body position in response to changes in the terrain. Standing allows you to move your centre of mass backwards or forwards quickly and easily. The trick is to keep sufficient weight at the back to maintain traction, but be far enough forward so you can still steer the beast and not flip it over backwards. The correct spot will see your hips a little forward of the usual sitting position. When you're doing it correctly, the front wheel will feel quite light. On relatively smooth terrain, you can get away with staying in your seat by edging forward onto the nose of the saddle (hardly comfortable though). Roll your wrists and elbows downwards to drag your weight further forward while keeping your upper body nice and low.
You want to create a 'power equilibrium' between your arms and legs, pulling up on the handle bars as you apply the power stroke. Your back wheel bites in as the bike rotates around a virtual pivot at the bottom bracket. Don't wrench the bike from side to side like a Tour de France champion - balance the "power equilibrium" by pulling up on the right hand as you push with your right leg and vice versa. The action is quite athletic - your arms should ache as much as your legs after a hard climb.