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 company, runs a limited service from Buchs SG station in Switzerland, via Schaan-Vaduz station (near Schaan) to Feldkirch in Austria. Trains only run a few times a day, which makes buses generally more convenient.
Buses run every 15 minutes from the train 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 where it's possible to catch a bus (see below) straight to Vaduz. Consult the SBB timetable  to find out what'll be 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 number 12 service runs from Sargans railway station to Buchs 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 5.80 CHF from Sargens and 3.40 CHF from Buchs. Consider getting a whole network day pass (12 CHF) or week pass (24 CHF) if you are making many journeys on Liechtenstein Buses, though two single fares (e.g. from Sargens 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. Numbers 11 and 14 head straight to Vaduz and number 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's 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. It takes little more than half an hour to drive from one end to the other.
The Art Museum 'KunstMuseum' has an interesting collection on the ground floor and in the style of Tate Modern has a changing modern exhibition on the first floor. Further down the street is the Liechtensteinisches 'Landesmuseum' which gives you a view of the broad history of Liechtenstein. A third museum in the main street is the 'Postmuseum' and displays the history of Liechtenstein's postal history. All stamps issued over the last hundred years as well as other objects are on display. The museum is free of charge.
The Prince's Wine Collection is available to view by a vineyard on the Northern edge of Vaduz. This is a 5 minute walk from the central square.
Excellent views of the surrounding area can be gained by taking the short walk up to the Castle, which hangs above Vaduz. The walk is gentle and goes up the side of the hill and through the woods and emerges at the side entrance to the Castle. Mind the grey displays along the road; they will teach you the history of Liechtenstein and the monarchy. It is not possible to enter the grounds of the castle, but walking around the perimeter is fine.
A short walk towards the river will offer visitors the chance to experience some great views of the mountains surrounding the city. The old covered bridge, which spans the Rhine River, provides an interesting way to cross the border between Liechtenstein and Switzerland. The unpainted, weathered wooden bridge is rustic in appearance. The bridge accommodates foot or bicycle traffic only; cars are prevented from approaching. Drivers may find it tricky to pull-off. Cars on this road are headed to the Swiss Autobahn, a few hundred meters across the river directly west of the bridge. Please use care; these motorists may not tolerate the casual traveller on a busy road. There is no means to access the bridge from the west by car. The road that would appear to lead to the western end of the bridge is the aforementioned Swiss Autobahn.
From the center of Vaduz, follow Zollstrasse (towards the football stadium) until you reach the river. There are no border checks.
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.
Frankly, you'd be mad to spend the night in Vaduz when you could ascend into the mountains and enjoy the breath-taking views from places such as Triesenberg or Malbun.