A good place to start is with the library. They usually have a variety of books on beginning quilting, often with step-by-step photos.
Most quilters today use a machine, but many also hand piece. It is not bad to use a machine -- just a different method which makes piecing much faster.
These days, for quilting, you really want to have a cutting mat, rotary cutter, and a 6"x18" acrylic ruler to cut pieces. You should ask for these for your birthday too. JoAnn's is a good place to look for beginner sets of these tools.
What price range are you looking at for a sewing machine? If under $200, then I would suggest this one:
http://www.amazon.com/Janome-Jem-Gol...dp/B000FLH2VE/
Janome is a good brand and this machine is lightweight and easy to take to classes.
In terms of learning how to use the machine, it would be really helpful if you could find a family member or friend who knows how to sew to spend a couple of hours with you. If no one in your family knows how to use a sewing machine, ask around to your friends. Someone's mother probably knows how to sew.
Edit: Well, I just read the posts on the second page! Even if you can't check out books from the library, you can look through books to your heart's content while sitting in the library. Those books will give you a good idea of the steps required to make a quilt. Many will also show how to use a ruler, rotary cutter and mat to cut quilt pieces. Some will also explain how to make quilts by hand, cutting out pieces using homemade templates and hand sewing the pieces together.
If your family buys you a sewing machine at a dealership rather than off-the-shelf (say, at Walmart), they can negotiate for lessons. Dealerships routinely offer lessons with new machines, but may be persuaded to offer lessons even with a used or vintage machine (which are often a better deal).