My grandmother taught me how to sew a loooong time ago. As a kid I made almost all my own clothes, made my own wedding dress, etc, but now I only sew stuff that gives me a big bang for a little buck. I think the most rewarding thing a new sew-er can do is to make lined curtains or valances. Almost all popular styles today can be made as one variation or another on basically sewing a pillowcase, and you don't need any lessons beyond the simply learning how to use a straight stitch on a machine for that. Much easier than starting with a pattern to sew a dress.
Cut out a rectangle, put the right side of your nice material against an equally sized rectangle of lining, sew a seam across the sides and top, iron the seams open, clip the corners, turn the "pillowcase" rightside out, iron everything flat, and handsew a hem by turning up the raw edges of the material and lining as one unit, and then catch the thread just in the lining. Depending on the look you're going for, you can then sew a rod pocket (using a seam ripper to open the top of the sideseam), pleat the top in lots of ways, etc. Ask at the fabric store - you'd be surprised at how easy it is to make a pinchpleat, for example.
Although there are slightly more professional ways to get the job done, you can make really beautiful professional looking drapes using this simple method at a fraction of the cost of having them made. Fabric stores have beautiful remnants and great sales. I've gotten small amounts of exquisite $30 a yard fabric recently at Hancock for less than $6 a yard as a remnant and nice 54" wide lining for less than $3 per yard. That translates into making a professionally full valance out of gorgeous fabric for less that $15. When you compare that to most of the skimpy ready-made valances out there, you can't go wrong.
A valance is a starter project that can really instill confidence, and even if you screw it up completely (which you won't), you aren't out much time or money. Make a few coordinating pillows and you can pull together a really decorated look. (Although sewing the cording around a pillow is a little trickier for a novice than you might think, so you might want to skip the cording the first time.)
Hope this helps - sewing is pretty easy and I think you can pretty much teach yourself.
What brand is a good one? Singer, Pfaff, Brother, something I've never even heard of? I just want a simple beginner's machine. Is it a bad idea to buy at a "chain" store or should I stick with my local sewing machine shop? What about eBay?
Good luck!
I'm feeling confident! 
Mad4theMouse, that made alot of sense.
Can anybody tell me what a serger does?
