Another option if you want to avoid PEK airport (as I do) is ICN. If staying at a hotel in UB city pre-arrange for a ride from them from the airport. It will generally cost $20 USD. That's more than a "taxi" by about twice, but worth the peace of mind. If you've never been there before the throng of questionable people just outside baggage pickup can be intimidating. Oddly, the airport is the only place I've felt really vulnerable in UB.

Once in town any car is a taxi, just wave someone down. Generally it's $2-3 to get most places. But if the driver doesn't display immediate understanding of where you want to go, get out and try another. English is just beginning to take a foot hold there, and most people speak only Mongolian.