Vaduz is the capital of Liechtenstein, but not its largest city: Schaan is slightly larger. Still, it's home to the Prince's castle and his museums, and thus the main point of interest for visitors to this small country. In part due to Liechtenstein's only-recent prosperity (i.e. post World War II), most of Vaduz consists of modern buildings, and it lacks the "old-world" feel of many European capitals.
ÖBB, the Austrian Federal Railway, runs a limited service between Buchs SG in Switzerland, via Schaan-Vaduz station (near Schaan) and Feldkirch in Austria. Trains only run a few times a day, making buses more convenient.
Bus n°12 runs every 15 minutes from the rail station at Buchs (the main Swiss town on the Liechtenstein border) to Schaan and Vaduz. Tickets can be purchased on the bus for 3.40 CHF and it only takes about 10 minutes to Schaan and another 5 to Vaduz.
If you're coming by rail from Switzerland, it may be quicker and cheaper to take the train as far as Sargans (rather than Buchs), from which it is possible to catch bus n°11 (see below) straight to Vaduz. Consult the SBB timetable  to find out which will be the quickest when you're travelling. There are lockers at the Sargans station so you can leave your luggage there. The link  provides a plan of the station showing the lockers and where to catch the bus from.
The Liechtenstein Buses n°11 service runs from Sargans railway station to Feldkirch railway station via central Vaduz and Schaan railway station. It leaves from outside each station approximately every 20 minutes. The buses are yellow-green in colour. A fare to Vaduz is 8 CHF from Sargans and 3.40? CHF from Buchs. Consider getting a whole network day pass (15 CHF) or week pass (24? CHF) if you are making many journeys on Liechtenstein Buses, though two single fares (e.g. from Sargans or Buchs to Vaduz and Vaduz onward to Feldkirch) cost less than a day pass.
From Feldkirch railway station in Austria, look for the distinctive off-yellow Liechtenstein Buses. N°11 and 14 head straight to Vaduz with bus N°14 the quickest and n°13 goes to Buchs railway station, by-passing Vaduz, so you'll have to change at the Schaan railway station interchange.
You can also drive into the town - it is well signposted. There is plenty of parking.
Vaduz is very small and walking around the city and the areas around it will not take very long.
The best way to move around Liechtenstein is by car or bus, with all villages linked by bus. It takes little more than half an hour to drive from one end to the other.
FC Vaduz is the soccer club in Vaduz.
The main shops in Vaduz sell tourist trinkets all branded in Liechtensteinian and Swiss colours. There are plenty of flags, t-shirts and cuckoo clocks available. People who enjoy collecting passport stamps are able to get an official Liechtenstein Tourist Office stamp at the Tourist Information office. The cost was 3 Swiss Franc (CHF) or €2,50 in July 2013. This is especially unique as there are no border crossings at either of Liechtenstein's frontiers. Postal Stamps and postcards can be bought at the post office opposite the tourist office as well as most other shops.
There is also a small retail village between Vaduz and Balzers. This is home to a McDonalds, and a sports clothes shop among other things.
The main square is behind the bus station in the midle of Vaduz. There are a number of cafes and restaurants offering hearty Liechtensteinish / Swiss / Austrian fare at reasonable prices.
Liechtenstein isn't a cheap place to eat. If you want something budget and have a car, drive to Feldkirch just across the Austrian border.