Tashkent is reasonably well-connected to Europe, Asia and the Middle East. Samarkand is Uzbekistan’s second-biggest airport with a number of international flights. Smaller airports are sometimes connected directly to different Russian cities. Since 2017, Tashkent has gotten connections to all Central Asian countries (except Turkmenistan).
Uzbek Airways is generally not considered to be a good airline. But it has a quasi-monopoly on flights to Uzbekistan, and a full monopoly on domestic flights.
Tashkent airport was known as one of the worst in the region for security checks and long delays, but this has improved markedly since 2017. Almaty and Bishkek still offer better options price-wise, although you will probably need to transfer. If you are doing a multi-country trip, consider starting and ending your trip there.
Online booking an Uzbek Airways flight is possible nowadays. If it does not work out for you, check this page for timetables and online booking of domestic flights.
Tashkent is connected by airplane with Andijon, Bukhara, Ferghana, Karshi, Namangan, Nukus, Samarkand, Tashkent, Termez and Urgench. The Bukhara-Urgench flight could prove useful.
Flights by Uzbekistan Airways are generally good value for money, but long waits, baggage checks and bureaucratic airport nonsense might still persuade you to take the train (it’s getting better though).