Uzbekistan Airways operates regular daily flights (at least two flights a day) from Tashkent (majority of fights on Airbus 320, with a small number on IL 114 and Boeing 757), flying time 1 hour 40 minutes. Ticket cost (as of September 2013) was 210,000 sum (approximately $75-80) for one way. Tickets can be bought from local ticket offices in Uzbekistan. Now tickets can be bought on the internet as well, on the usual travel search engines (you can use skyscanner.net). These flights depart from Terminal 3 (the domestic terminal) at Tashkent Airport. Uzbekistan Airways has invested in modern aircraft in recent years, so these flights are usually very comfortable. Flights on IL114 take slightly longer, about 2.5 hours.
There are direct flights twice a week from Moscow and St. Petersburg by Uzbekistan Airways. Two Russian airlines also fly directly to Urgench: S7 Airlines from Moscow, Rossiya Airlines from St. Petersburg.
During the tourist season (spring and autumn months) Uzbekistan Airways operates direct flights from Milan and Paris to Tashkent with a stopover in Urgench. Please check Uzbekistan Airways time-table for flight schedule.
There are trains from Tashkent to Urgench every day except Tuesdays.
The train Tashkent-Urgench operates Wednesdays, Fridays and Sundays. Furthermore, the service from Tashkent to Saratov stops over in Urgench (departure from Tashkent on Mondays and Wednesdays), as do the Tashkent to Shavat trains (Mondays, Thursdays and Saturdays). The train journey takes about 18 hours.
There is also a weekly service from Bukhara to Urgench on Wednesdays and Urgench to Bukhara on Thursdays.
Train has become the main way to travel to and from Urgench for local people. In the last few years the Uzbek Railways Agency has significantly upgraded the trains and installed air conditioning in carriages.
If you're really budgeting your cash, you can catch a bus to Urgench from the Hippodrome station in Tashkent. The good news is the journey doesn't take much longer than the train (20 hours) and the cost is comparable to train and the buses are available daily, at multiple frequencies. The bad news is you'll be sitting in a cramped space without toilets (the driver decides when to make a pit stop) and minimal ventilation (forget about air conditioning). So, it is much better to travel by train with a bit more advance planning.
There are daily buses from Bukhara to Urgench, leaving from Bukhara Avtovoksal. The buses have no air condition. The journey time is about 8 hours and the price about 15.000 UZS on way [Sep 2012] . There is no fixed timetable, the buses leave, when all seats are occupied.
Inter-city "taxi" services are essentially a collection of informal drivers who wait to fill up their cars with passengers and then drive them off to their destinations. They usually charge per passenger; however, you can buy all the seats in a car (typically 1 in the front and 3 in the back) if you're willing to spend the cash. From Bukhara, the next closest Silk Road site, the 460km trip in a shared taxi should cost between 50000-80000 sum per person [Sep 2012]. The price can sometimes depend on the type of vehicle you're negotiating for, with Daewoo Ticos (think Ford Fiesta) costing less and Daewoo Nexia and Matiz brands (think Honda Accord) costing a bit more.