At the moment, if I recall correctly, dwarves don't care about their clothes, so you can just let them rot off their backs. This will be fixed eventually, though.
Hmm. Options for making clothes... you'll have to either use pig tails, spider-silk, or leather.
Pig tails would require some farm room, but have the advantage of having other uses. They also require a few more steps than the other methods, I think... you have to plant, collect, process, weave to cloth, and then make into clothes.
Spider silk is actually surprisingly easy, since most of the steps can be handled directly at the weavers. But unless you can get tame spiders (which I never managed), they're going to be slightly unpredictable, and unless you clear out absolutely huge river areas I doubt you could get silk fast enough to keep a large fortress clothed.
Leather is the toughest option, since you either have to raise and slaughter animals, or hunt. Raising and slaughtering animals is, in theory, almost completely effortless at the moment once you have your 'seed' beasts... it'd take forever to build a large enough population for them to reproduce at a decent rate, but once they do you could get leather easily.
Of course, the ease of raising beasts for slaughter currently comes from the fact that they don't need to eat, which will be fixed eventually, too...
Hrm, once clothing unhappiness is in, there will probably be clothing happiness, too, so you can make your dwarves happy by providing them with fine clothes. I assume they'll like silk more... will there be dyes to produce clothes of specific colors? Would some dwarves prefer one color over another? It could be tied to their material preferences... a dwarf that likes sapphire could prefer a sapphire-colored shirt.