I have to agree with others here that patience and consistent peddling are the rule for building strength for climbing. 20 years ago I used my Ross Gran Tour with it's 12-spd double crank and climbed all hills without stopping. All of them, including one 5-mile-long monster. Some are steep, and some seem never to end, such as those that appear to top out, only to continue after a very short semi-leveling. These days, since I'm way out of shape and 50lbs overweight, I can't get up most of those same hills with a triple crank, even on my very-low-geared recumbent.
Last year I used my mountain bike all summer and finally, at the end of the season, I was able to ride all the way up a nearby hill at the end of my ride just before getting back home. Practice and patience is crucial. You're using muscles that you don't always use for this, and using them in ways that you don't normally use them. In the end you'll prevail, and then it will start to get easier. I recommend doing your hill ride about once every three days, so you have time in between to recover fully. Muscles will not, under any circumstances, grow until AFTER they fully recover, so it's imperative that you give them time to do so, especially at first. Otherwise, your progress will be infinitely slower. Also, during off-season times, I'd recommend doing some weight training to strengthen your legs. Leg presses, curls, with variations of each will benefit you greatly, and you'll be stronger at the start of the riding season to boot.
Enjoy the ride above all....Mike