Extensive guides about getting around Uzbekistan with car, bus, taxi, train, bicycle, airplane etc. have been written, see the links below. This page serves up some general recommendations.
Getting around in Uzbekistan
Trains are an easy and comfortable way to move between the big destinations of Tashkent, Samarkand and Bukhara. If you are travelling independently, booking in advance is still a hassle, though. To leave as quickly as possible, a shared taxi or minibus is a fast and cheap alternative. Buses should be avoided where possible, it’s not an efficient way to get around.
Flying is a time-saver between Tashkent and far-off Khiva and Termez, or possibly Andijan. Winter has little effect on transport in Uzbekistan, almost everywhere is accessible year-round.