There are some things you can do to be a better climber

1. Learn to pedal in circles - pull up on the pedals as well as pushing down. This does require either toe clips or clipless pedals obviously. And learn to spin - to get a smooth pedal stroke you pretty much have to be spinning. Practicing on a stationary trainer will help strengthen your leg muscles and make this easier.

2. Learn to climb standing. Now, some people like to climb consistently in the standing position, while others just use it to rest their legs or when extra power is needed. You'll have to figure out which style you prefer. Standing climbing uses more cardio-vascular capacity, seated climbing uses more leg muscle. To climb standing you'll want your hands on the tops of the bars - at least on the hoods (I've heard unless you are Italian and famous pro don't climb in the drops ), stand up on the pedals pulling the bike forward as you stand with your hands and feet- this is to prevent your bike from shooting backwards into anyone who is following you. Gently rock your bike back and forth with your pedal strokes - don't force this - it should be a natural movement rather than a forceful rocking back and forth by using your arms. Standing climbs will be difficult to impossible if your bike is too big for you.

3. Go at your own pace and don't go out too fast on long climbs. You'll burn out fast if you try to follow someone who has a quicker pace than you.

This is pretty basice, but I hope it gives you some ideas.