Road Cycling: Help conquering hills

The comments provided so far are excellent! Climbing hills on a bike is no different than in a car--more power is needed to overcome the forces of gravity. In order to improve climbing power, you have to address 3 critical areas: strength, stamina, and mental focus.

Starting with mental focus, try not to tackle the climb as one ride. Instead, break it into smaller sections, or goals, that are more easily managed. This will help with the overwhelming feeling that can come with long climbs. Also, having smaller goals gives you a sense of accomplishment as you go up, up, up.

For stamina, you need to focus on breathing and efficiency on the bike. Look into breathing techniques because it's critical to keep blood gases equalized as you work. One technique to learn is cleansing breathes. You also have to build endurance. That comes from long, steady rides (and not on hills). Riding 60, 80, 100 miles will help climbing as much as power work will. With efficiency, you should also address pedaling technique. Make certain that you are spinning in circles! This can be practiced with single-leg spinning, which is just what it sounds like. Unclip one foot and rest it on the chainstay or skewer and pedal with the other leg. Keep cadence around 80 RPM. (Only do this on roads that are lightly traveled or on a trainer!!!)

Power work can be completed on hills or flat ground. For a good flat workout, find a long stretch of road and grind away--find a gear that is difficult to turn at a cadence of 50-60 RPM. Ride at pace--but ensure that the effort stays hard; going easy with a slow cadence isn't effective--for 3-5 minutes, depending on you fitness level, and then recover for 3 minutes with a high cadence (90-110), and then repeat 3-5 times. 

Hill workouts vary depending on your goal. A fun one that will build power and help your body learn to recover while under load is power bursts. The workout is pretty easy (relatively speaking!). Find a climb that takes about 5 minutes to complete. Start at the bottom in a relatively easy gear, again, this will depend on fitness, and spin up the hill at 80-90 RPM. After one minute, accelerate by raising your cadence 10-20 RPM and maintain that pace for 15-30 seconds. Then, drop back to same cadence that you were spinning at the bottom for 1 minute. Continue repeat until you reach the top. Turn around and ride easy to the bottom in order to fully recover and then repeat again for 3-5 reps.

Recovery is equally, if not  more, important as hard workouts. Don't over do it! Try doing intervals or other hard workouts only twice a weekly. Your body needs time to repair the damage and going too hard too often will defeat the process, effectively causing you to ride slower.

It really depends on what kind of hill it is.  Some rollers you just power through, short steep ones need a different technique and long mountain climbs another.  

 The biggest problems I see in novice cyclists are:

 1. Making the transition (from the flat preceeding the hill into the lower portion of the hill) 

2. Incorrect shifting choice or location of the hill

3. Not finishing the apex of the hill

A lot of takes practice and self knowledge and maybe some good coaching that can ride along side you.  Find a good vet racer in your area and chances are they'll be willing to pass some of their knowledge to you.