Do you just want to learn to decorate birthday cakes? Or do you want to learn to be a pastry chef and make scratch cakes, cookies, pastry, bagels, breads etc? There are a lot of decorators on CC that post (hence all the replies suggesting Wilton), not so many pastry chefs that post.
So, it depends on what you want to do. You could easily attend a few Wilton classes and get a job at your standard bakery or grocery store. If you are lucky and your city has it, you can take specialized classes from cake artists and learn more complicated techniques with fondant, gumpaste etc. You could buy a few books, study and experiment and learn to make flawless cakes from scratch. But I DON'T think you'd be able to learn how to properly temper chocolate or pull sugar to make show pieces unless you go to culinary school.