There's no way of knowing without knowing whose doing the work--you or a contractor, how much the permits are, what type of fixtures you're putting in and the like.

If you're doing it yourself, find out as much info as you can as to what each item costs, make up a budget and go from there. And speaking from experience, I can tell you from experience that it's going to cost more and take longer than you think it will.

Well we will not be doing any work-- a contractor will. I'm trying to understand how much would it cost for plumbing, installation and finishing of a 4 x 6 half bath (a commode and vanity) in a pre-existing space.

It's best to hire an architect to draft up a set of plans for contractors to bid on.

The best approach may be to call up some local companies and ask if they'd come out to look at the project. You'd probably get a good idea of cost after a few come to see it.