Relax! Smile! Breath! Spin! You can't climb efficiently when you have a death grip on the handlebars and are leaning forward. Try to keep your weight off your front wheel and more on the back. Breath easy and make yourself relax your arms, neck and shoulders. Don't sit in the saddle like you have a hanger in your jersey. The tension in your upper body takes power away from your legs. Just keep at it and you will get stronger.

I agree with Chicagogal in that it's half technique and half mental. I used to have anxiety attacks when I saw an upcoming hill but soon realized that it's never as bad once you get into it as it appeared when you were approaching it. I wouldn't look at the hill, just the road right in front of me so I wouldn't get overwhelmed at the task of climbing.

Remember there is a reward at the top---the downhill!