I would like to travel from Bregenz to Vaduz. The Austrian railway web-site only gives me rates upto Feldkirch Bahnhof. And it says I need to take a bus from there. Does anybody know which bus goes from Feldkirch to Vaduz, what's the frequency and if they will take Euros to buy the ticket?
According to Rome2Rio you can go by train from Bregenz to Feldkrich, and then either by next train (8 minutes) or by bus (40 minutes). Bus from Feldkirch to Vaduz leaves every 30 minutes, it goes to Vaduz center: ÖBB website
I can't find pricing information though. In LIEmobil I paid with CHF, but I was going from Switzerland.
The nearest railway station to Vaduz is Schaan-Vaduz station which is about a 45 minute walk from the center of Vaduz. Since the station is very far from central Vaduz and there aren't a lot of trains most people use the local bus system, LIEmobil (formerly Lichtenstein Bus). In their current timetable there's a useful map of the network and the note that they accept Euros in the bus.
The tariffs are complicated, if possible I'd find a clerk to talk to at the station in Bregenz, they can sell you the entire ticket you need including the part for LEImobil.
For travelling from Bregenz to Feldkirch there are two possible prices for the same ÖBB trains: the ÖBB prices and the regional transit authority (VVV) prices. Whichever is cheapest will depend on any age or group-based discounts or return travel plans, it's best to speak to a ticket agent at the station they can issue either type of ticket.
If you choose to take the train onward from Feldkirch to Lichtenstein the same Austrian tariffs apply, since the ÖBB rounds the few stops in Lichtenstein up to being part of the regular Austrian system.
If you choose to take the bus onward from Feldkirch to Lichtenstein you'll need a ticket that's valid for LEImobil. You can either purchase a special VVV+LEImobil Kombiticket for your whole journey starting in Bregenz or you can purchase a LEImobil ticket for just Feldkirch-Vaduz from that bus driver in cash (in Euros or Swiss Franks). In my personal experience, the fair boxes of LIEmobil are frequently broken, especially when you present the driver with Euros, and you get a free ride if you don't already have a ticket for their buses.
TL;DR: taking the ÖBB train to the LEImobil bus that leaves frequently from Feldkirch during daytime hours will get you to Vaduz center most quickly. Just take Euros and tell the first person you buy a train ticket from what your whole journey is and they'll tell you what to do.