Being funny is definitely a learnable/teachable skill. I have seen some very unfunny people develop their humor skills with great effect.
My suggestion is to start reading John Kinde's humor skills blog at
Humor Power. Also be sure to sign up for his free newsletter. He shares many insights on the nature of humor, breaking it down step by step. John is a local friend of mine who has an amazing wit, especially in his skill with spontaneous observational humor. He also manages a local comedy improv troupe in Vegas.
The next thing is that you need to start practicing. John runs frequent humor contests on his blog where he accepts reader submissions. Start competing in those, and see if you can make the top 3 now and then. Erin and I have contributed to some of these contests as well, and I've helped judge quite a few of them.