For many of us, sewing brings up memories of poorly crafted aprons made in high school to the insane specifications of a slightly-evil, slightly-crazy home ec teacher.
But, in today's economic climate (if you have expensive tastes), sewing can be the way to go. I'll grant, you can probably shop end-of-season sales or discount stores and dress cheaply enough that sewing does not make economic sense. But if you like a little flair in your wardrobe, or if your taste runs more to Anthropologie than to Target, being able to sew can be a godsend.
There are a lot of ways to begin sewing. Most local sewing machine dealers offer sewing classes for any level from beginning to advanced. (Oh, and if you are shopping for a sewing machine, go to a dealer. They often have used machines they can sell you that will get you started for a reasonable amount of money. New machines that cost under $100 are about the quality of the toy sewing machines that were sold when I was a kid in the 70s.) Dealers will help you learn to use your machine and will repair your machine, should the need arise.
If, though, you already have a sewing machine, and are a veteran of the poorly-made-apron-in-high-school experience, you can just start sewing. (Oil your machine first, though!) One place for traditional sewing instructions, ideas, and patterns is Sewing.org. The instructions they provide are clear, thorough, and very do-able. Oh, and free.
If you are more of a just-do-it kind of person, though, check out T-Shirt-Surgery. This is a Live Journal Community of people who "reconstruct" clothes, often t-shirts or thrift store finds. What they lack in knowledge, they make up for in imagination. They proudly show off their creations, and some of them look really, really good. I would wear them, and my clothing is pretty conservative.
If you need a reference book that you can hold, though, my favorite is The Sewing Bible: A Modern Manual of Practical and Decorative Sewing Techniques. I bought it as soon as it came out. It is wonderfully illustrated and, best of all, the instructions are clear and do not assume that you have tons of knowledge already.