Karen....
There are a number of factors contributing to positive hill climbing.
Like a number of folks have already said, you want to be in a comfortable position. Also it can be useful to slide back ever so slightly in the seat and lean forward a bit - this just gives you a bit more leverage and ability to apply force to the pedals.
Standing while climbing is easy to do, but not easy to do efficiently or right. You will make more power while standing but it will also jack up your heart rate and fatigue you very fast. Many recreational riders waste huge amounts of energy swaying the bike wildly side to side, etc. I do 90% of my climbing while seated.
Pacing is an aspect you want to consider too. Many, many people will start going up hills as fast as they were going on the flats....so of course, shortly thereafter they rapidly tire. Pace yourself sensibly, start out at a pace that feels a little slow, so that near the end you can build up rather than struggle and gasp to the top.
Another thing that is important is gearing. Most people will pedal at some rate > 70, let's say, in the flats. You want to have a low enough gear, on a hill, where you can keep your cadence higher. Higher cadence/low force is easier to maintain for a longer period, than a low cadence/high force combo.
Finally, for all the mystifying or theories about climbing, once you have your basic technique/position/gearing right - going faster up hills is as simple as power to weight ratio. More power and/or less weight = better hill climbing.



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