The contract (which was made with Volvo, not Ford) will start with a small fleet of cars by the end of August and add 100 Volvo SUVs modified with Uber's technology by the end of the year. The company promises completely redesigned cars on the road by 2021, which seems to be the magic year for all car companies gunning to put out self-driving models.
As it stands, however, cars without a human companion aren't due to take over anytime soon, since researchers only just figured out how to trick crucial sensors into working properly when weather is anything less than immaculate. (Vox brings up a good point, though: just because the technology will eventually be there down the line doesn't mean the laws to let it happen will be.)
It appears that, on the rider's end, not much will change, save for being greeted by an "engineer" sitting patiently and blankly in the driver's seat, with a note-taking nerd in the passenger's seat (hehe, just kidding -- they're there to take control of the wheel in an emergency, and QA and monitor the car, respectively). Whether that's preferable to the typical curmudgeon of a driver talking to a friend on the other end of their cell phone, it's too soon to say (also kidding! Pittsburgh is full of very nice people).