I hate to sound like a broken record but the only way to learn to ride up a hill fast is to ride up a hill fast, and in between do lots and lots of high resistance and or high speed intervals on the flat.
If you have a gym locally, do some leg presses and gradually increase the weight you are pressing. I have found that the machines where I push the weights away from me, not where I push my body away seem to work the best for me but experiment with the resistance machines. Don't forget a bit of hip stability in the form of abductors and aductor muscles ( pushing your legs apart, and pushing your legs together. Also consider some front and side planks for core strength.
But mostly just ride the hills and enjoy yourself. If you do enough hill intervals you will get stronger and faster.
have fun.
marni