The most important thing I learned about hill climbing is: if you are going downhill and you see a steep hill coming up in front of you, don't slow down or stop pedaling. Get as much momentum as you can to glide half way up the hill and keep pedaling until you have to shift down. Then get into your lowest gear as quickly as possible and spin for the remainder of the hill. Don't wait until you have lost all momentum to shift down.

This doesn't work on really long hills when all momentum is gone. Then you need to find the sweet spot between leg muscles hurting (high gear - pushing) or breathing too hard (low gear fast spin). Then keep at it as long as you can.

If you start weaving, it is not a sin to walk your bike for a short while. If it even slightly levels out or the grade gets less intense, then get back on the bike.

Using these techniques, I have gradually improved my hill climbing. I can get up hills that I used to walk. And we have really big hills here. The small hills are easy now.