Hopefully you read tips 1 and 2 ... and have taken those to heart. Having strength in your legs from riding and the right fuel to power them is important. But there are also some techniques you can employ to get yourself up that incline. I have picked these up from a few places on the web, but mostly from a book entitled "Get Fast" by Selene Yeager.
For some of this to work, you will have to be "clipped in" or at the very least have toe cages.
First, scooch back in the saddle. I think most people's instinct is to lean forward and into the hill like you are angrily attacking it. However, when you lean forward you are activating the hip flexors and quads in the front of your legs. Those are relatively big muscles, but the glutes on your backside are bigger - and therefore more powerful. By schooching back you can activate those larger muscles. I think you will be surprised at how much more strength you will have access to when you are back on the saddle. You will see some riders get up and out of the saddle on a hill. What I have read - and experienced - is that is an advanced technique. So I'm leaving that for later.
Second - and this sounds silly - but consciously pedal in circles. You may think "how else would I pedal, because my foot has to go in a circle?" However, I think the novice instinct is to push down which leads to a punching motion with your legs. By only pushing and not also pulling through the whole circle, you are basically wasting half of the stroke. And when you are going up hill, you don't want to waste any precious energy. Also when you push down you are probably pointing your toes down. Pulling through with your foot flat will give you maximum power. I find that I am often pulling through the stroke even more than I am pushing the pedal around.
Third - and really don't laugh until you've tried it - be Zen. RELAX, BREATHE and THINK LIGHT. Let go of the death grip you probably have on the handlebars. Tension in gripping the handlebars is wasted energy. Try to control your breathing. Rather than going completely anaerobic and letting your heart rate sore, try to breath in deeply through the nose and exhale fully through the mouth. By "think light" I mean literally "think about something light". Envision a floating feather, a fluttering butterfly or a big puffy cloud. Any good sports coach is going to tell you that visualization can help your game. Get the negative "I can't" thoughts out of your mind and try this. Hey, you don't have to tell your fellow riders what's going on in your head.
Fourth - be prepared and then shift, but not too much! It's always a good idea to be looking ahead on the route. So hopefully you see the hill coming. When I see a hill coming I look down and check my gears. Depending on how steep or how long the hill appears to me dictates how much I will shift up (making it harder to pedal) before I get to the start of the incline. On a steep or long hill I try to give myself as many gears to shift down into (making it easier to pedal) as I can, in case I need them. I know I'm not powerful enough yet to do most inclines on the big chain ring, so I'm usually shifting to the small chain ring and the smallest sprocket I can handle on the cassette in the back in prep for the climb. Then I follow tips 1, 2 and 3 and only shift one gear at a time when I feel my cadence starting to drop. I try to not wait too long to shift, but I also try to not shift too soon and start "spinning" because that causes a serious loss of power and can really sap your momentum. Selene suggests finding your "sweet spot" cadence and they trying to hover just 10% below that so you have a little boost left. Remember high school physics? Bodies in motion tend to stay in motion but bodies at rest tend to stay at rest? You want to continue to be the body in motion on that hill. Watch a really good cyclist in our group go up any of the hills on our routes and I will bet you their cadence doesn't change much from bottom to top. They are shifting as they need it in order to keep their cadence and speed as constant as their legs will allow.
A couple of these things may sound silly, but I am telling you that the first time I applied all four of these techniques on a hill that regularly dropped me, I ended up passing the ride leader by more than a bicycle length. The ride leader knew my riding and was pretty surprised, but no one was more surprised than me.
Now this isn't fool proof. I will confess that I can do all of these things on another day on the same hill and fall back. But ya' know, some days you're the windshield and some days you're the bug. Every athlete has good and bad days. But just this morning I was down on the drops on a hill and my arms/hands were so relaxed they were barely hanging onto the handle bars. My legs were doing all the work. At one point my breathing was getting labored and as soon as I started to focus on that, I got the last bit of strength to get up and over.
What is really cool is that there are parts of the routes that I used to consider hills, that are now merely inclines that I can power up and over without really noticing. Sometimes I don't even need as many gears as I used to. Part is due to the strength I have gained in my legs and part is due to regularly applying these techniques. But what is also cool about cycling is that some of the hills are still hills. So I still have a challenge.
P.S. I dare you to not hum the title song sometime today. And if you're too young to know what I'm talking about, don't tell me.