Enchanting is one of the most costly professions to level. (Don't thump me with the D?E stick just yet, ohmikeghod ;D)
If you're patient, you can level enchanting with very little out-of-pocket cost. Gathering cloth to convert to greens that you can D/E for mats to skill up helps. Running dungeons for greens can help a bit, but the drop rate on said greens is typically not much better in dungeons than it is anywhere else...the only real difference is that the density of mobs in dungeons makes it seem like you are getting more greens. By the time you reach the 250-275 mark for enchanting, your cost is going to spike enormously. Fortunately, WotLK eliminated the need to take the TBC formula routes from 350-375 because that stretch was also horribly expensive. Once you get to 350, it's not too bad. There are lots of WotLK formulas that don't require too much by way of mats and give good skillups for some time. As well, if you've got an herbalist or a scribe alt, you can get cheap vellum to put your enchants on as you skill up and (at worst) mitigate some of your losses or (at best) generate a bit of a profit.
You can also cruise the auction for underpriced greens to offset your leveling costs. If you're patient and play it smart, you'll spend very little and if you get a decent cycle of greens coming in from low bids, you can turn disenchanting into a reasonable income generator.
If, on the other hand, you decide that powering enchanting from 1-440+ is the way you want to go, it's going to cost you a small fortune.