I recently found that I'm not that great on hills when it comes to competition (to put it mildly).
However, what others have said is true, you will get better and whilst there will always be those who are better climbers than others, it is your own improvement that counts. You can't be good at all aspects of cycling and many different aspects there are.
I'm not a natural climber either but I've come on leaps and bounds by my own standard because I've kept at it and not shied away. Each climb has its own particulars and whichever poster recommended doing the same route is right. You'll even begin to remember which gear for which part of the climb and as you get stronger turn a higher gear, which is symptomatic itself of improvement.
Despite not being a natural climber I'm doing the Etape in July, taking in four Category 1 climbs in the Pyrenees and of course it's going to be tough. But, despite this I've learnt to relax a lot more whilst training (something you can't do in a race) and I'll take each and every mountain in my own stride, concentrating on breathing and a steady rhythm. I know, despite, the length of the climbs that there will not be anything steeper than what I am used to here in the Mendips (the Mendips have the slower, gradual climbs like Cheddar Gorge and Burrington Coombe but also many other far steeper affairs like Ebbor Gorge with gradients far surpassing anything in the Pyrenees) and so the game becomes one of endurance more than anything else and getting used to dealing with lesser gradients over a far longer period of time. Huffing, puffing, giving it your all in the first few hundred yards isn't going to work when you've got another 19km to go to the top, so I can't stress enough how important 'relaxing' is. And yes, I know it sounds ridiculous, relaxing? But it will come.
Start in a lower gear than you think at first, don't think because you could push a bigger gear that you should, find a position on your bars that suits you best and take it steady - you are not racing! You are gradually improving your fitness and your ability all the time. Don't be scared to get out of your saddle when it feels right and don't even think that you need to do the whole hill in such a position, sit back in as low a gear as possible if you need to, and grind away. It will get easier.
If you're on a double, I heartily recommend an 11-28 ratio cassette. Best of luck pal.