Every car is a potential taxi in Tashkent, but essentially there are two forms: licensed cabs and ‘independent’ cabs. The former have little roof-mounted ‘taxi’ signs. The latter are just average cars driven by average dudes.
Independent taxis generally leave it up to you to pick the price, which is fine. As long as you don’t insult them with your offer, they will usually accept it. The minimum fare for a short hop is 3000S, but this can be as little as 1000S if there are other passengers in the cab already (as will often be the case). Longer trips will cost 5000-10,000S: unless you're supremely confident of offering an acceptable amount, always agree a fare before you get into the car.
Licensed cabs – especially those waiting outside bars and hotels – are a different beast, so always agree a fare in advance and expect rates to be a little higher.
Cab drivers tend not to know street names (and when they do, it's generally the Soviet-era ones), so use landmarks – big hotels and metro stations work best – to direct your driver to your destination.