Originally Posted by
relyt
You need to try to maintain your cadence. Shifting gears is how you do that. Try buying a cheap cyclecomputer with cadence and experimenting with it. When you hit a hill, unless it is a really short one, you should gear down until you can keep up the same cadence you would on flat ground. It looks like your bike has an 8-speed hub, so you should have an easy time shifting, because you don't have a front derailer to shift.
I have a monster hill going and coming back from my commute - relyt put into words what I do to conquer that w/o burning myself out. Check your spin on level roads, where you're most comfortable at spinning - you want to maintain that spin rate going uphill. So, as you begin climbing the hill start dropping down one gear at a time until you are spinning at the same rate you would be on the flats. Hope that makes sense...