Okay, I said that you didn't need to spend a lot of money to get started sewing (and you don't) but Bellaleigh brought up a good point — if you aren't near a good fabric store (and sadly, fewer and fewer of us are) you won't be able to do the "go wander around and touch everything" learning that I recommended yesterday.
But, if you have a spare $30-40 or so, you can get one of Julie Parker's books. That's All About Wool there, but she also has one on cotton and one on silk. The genius of these books is that not only do they give you the usual "how-to-wash-it, where-does-it-come-from" info, but they also tell you how difficult it is to sew, and what you can expect to pay per yard. Plus, swatches of everything, so you CAN feel them!
This is the kind of book that I would hint mightily to someone that I wanted for a birthday/holiday present, perhaps by saying, suggestively, that if I knew how to SEW, *someone* might get a handmade whatsis. At some undetermined point in the future.
Another way to get your hands on fabric is to sign up for a swatching service. For the same amount of money ($30) you can subscribe to Sawyer Brook's high-end fabric swatch club: I've never done so because I am notoriously cheap about fabric (other than Liberty of London) and Sawyer Brook is a bit pricey. Also ringing up at $30 is Vogue Fabrics' (my "local" store) swatch club.
You can also sign up for the Fashion Fabrics Club swatch service, which is much cheaper (about $5). Or you could just buy some fabric from their site, since that seems to have gotten me on the mailing list. Their swatches are quite small, and may be hard to match up with the descriptions (I've never yet been able to open the envelope without spilling them all on the floor), but it's a start. (Also, they tend towards the rayon end of the spectrum.)
In addition, if you are looking for one specific kind of fabric, many of the big independent fabric stores (like Britex, and possibly G Street, although I can't find it on their website) will take a swatch request. The one time I did this (I think it was in 1997) I was looking for white cotton with a red cherry print, so I called up G Street and Britex (now they only do this kind of thing by email, snail mail, and fax) and told them exactly what I was looking for. Britex had only one possibility, so I bought it sight-unseen (I still have the dress, too, I'll have to dig it out and photograph it for y'all). Swatch requests run about $5-10, depending on what you want. Thai Silks sells sample swatches, too, but their sets range from $3 to $40.
So, if possible, it's best to rummage around a real store, but if that's not an option, a moderate amount of money can get you a big box of little scraps of fabric to fondle. Also, I know there must be more stores that do this, so if you know of some, please leave them in the comments!