As I read in Wikipedia Salar de Uyuni is far away from other cities.
Can I reach it from Potosí or Sucre?
How long does it take?
I would prefer to take a train. Is there a train route at all?
Most tours to Salar de Uyuni start from Uyuni town, you can get there both by train and bus from further north in Boliva.
We took a bus from Potosí in the morning and arrived in the mid afternoon, at least 5 hours. Nice landscape but bad roads, our bus broke down twice. From Sucre you can go via Potosí, but I am not sure whether you can do the whole way from Sucre to Uyuni in one day(light) trip.
The train leaves from Oruro, a pretty dull town between La Paz and Potosí. Even though I prefer trains as well, the reason why I did not take it was its timetable. It either leaves at 15:30 or 19:00 arriving in Uyuni at 22:20 or 2:20 respectively (info in Spanish). Uyuni is a bit rough around the edges and I did not want to arrive there in the dark. I don't think it is unsafe, but we still had to find accommodation and book a tour to leave the next morning. You really don't want to spend two nights in Uyuni.
Photo credit: Peter Hahndorf
Actually, you can reach it easily from three different directions/starting points.
From Chile, you'd be departing from San Pedro de Atacama.
From Bolivia, either Uyuni or Tupiza.
There IS a train, from Calama in Chile, but it's so unreliable and nobody knew if it was even running. Although while driving from Uyuni to La Paz at night, I did see it going past...
There is also a train on the Bolivian side, from Oruro to Uyuni, which takes about seven hours.
I recommend Tierra Mística, the company we travelled with. The guide could only speak in Spanish, so we'd take turns attempting to translate his words, which added to the hilarity and bonding of the group. He was actually great. We heard many horror stories of cars flipping, losing wheels, and even our other truck broke down from the cold (July). But Miguel was great.
I've got four posts on my blog that may be relevant. Be aware that we travelled on the San Pedro de Atacama to Uyuni route. It's also possible to connect between any of the three starting points (Uyuni, Tupiza, or San Pedro).
It's worth noting that IF you are doing it from Uyuni, or any of the others really, it's worth getting into town a bit early, or arriving with other travellers - that way you can group together and bargain for a better rate on the tours. Fair warning though, spending time in Uyuni is not great. San Pedro, on the other hand - you could spend 3-4 days EASILY - there's a lot to do there.
Yes, you can travel to Oruro by bus from Potosí or Sucre, and from there you can take the train or bus to Uyuni. As Peter mentions it can be hard to find accommodation in Uyuni late at night so arriving earlier is recommended.
Oruro train station is on the road Velasco Galvarro slightly south of the centre of town. It usually doesn't open until a couple of hours before the earlier of the two trains leaves, so you'll want to find things to do if you arrive in town early.
In the station, it's not obvious, but you'll need to take a ticket from a machine to get a place in the queue when the desks open, and there is often not a roll of tickets in the machine when the station opens. In this case, find a guard to get the tickets, and it's probably a good idea to offer the first ones to those who may have been waiting before you.
There are a limited number of "ejecutivo" (1st) and "salón" (2nd) class tickets, and the rest are "popular" (3rd). Tickets are allocated on a first come first served basis. The higher class seats are definitely worth it if you're already tired from travelling to Oruro :)
Alternatively, there are many buses operating from Oruro to Uyuni, but they will all be bumpy, noisy and uncomfortable because the road is in extremely bad condition. Don't expect to get any sleep if you travel late at night.
To get a bus to Oruro from Potosí or Sucre, go to the bus station no more than a day early as tickets are not usually sold earlier than this. Bus companies "El Dorado" and "Trans-Copacabana" offer the most comfortable buses, though there are loads of others that are cheaper. There should be a clear list of maximum ticket prices displayed at both stations so you can get an idea of what constitutes a good price. You will also see people from the bus companies shouting destinations ("Oruro, Oruro, Oruroooo!) in the station entrance. They are liable to offer you a slightly discounted ticket if you negotiate and then take you to the company desk to buy it.
You can get there from Sucre, Potosí or Tupiza. They also have an airport so you have the option of flying in.
Source: I live in Tarija. I give tours of Tarija.