The way I was tought:
If you have a lathe, you can build a lathe.
(I.e. you need a lathe to build one; the lathe being the only tool known that can reproduce itself. Though a mill might come in handy too?)
Personally, I wouldn't bother building one. The ones for woodworking are ridiculously cheap (in price and quality, BTW), the one I have here is about 100$.
Metal cutting lathes, I'd say have a look around at your 2nd hand machine dealer. Last week I saw a very nice Cazeneuve. Just what the doctor ordered, and the price wasn't too bad either. Now to find a free spot in the shop...
Once you have a lathe and learn how to use it, you'll hit yourself on the forehead for not having bought one 10 years earlier...
As far as building one goes, again, look around for a 2nd hand. I think you'll get much more value for your money that way than building one. Like the others said, the headstock and tailstock aren't that difficult. But a good crossrest (stable). Plus a good solid frame. Lead screws. A Norton-gearbox would ofcourse be out of the question (but is SO nice to have...)
If you insist on building one, there are plenty of designs around for constructing your own; a quick google search should give plenty of results. But, again, you'd probably need a lathe (or access to one) to build one. Plus a mill perhaps.
Peter.