Generally you would connect a pedestal sink and a sink in a cabinet/vanity the same way. A pedestal you have to be more careful with because the pipes need to line up better. I find it odd, though, that the waste pipe is coming out of the floor. You will need a p-trap in there, and generally waste exits horizontally into the wall and then down

Does the drain pipe come up right against the wall? If it does maybe the plumber was thinking you would have a stud wall. If that is the case then the drain pipe would come up a little and then stub out of the stud wall.