There are several buses to and from Uyuni, and trains too.
I found the Lonely Planet not very updated about transportation. You can get more information asking the agencies in Avenida Arce.
The bus trip from Potosì lasts about six hours, when you are not involved in bus accident on the road. We had to wait the police, in the middle of nowhere, for more than two hours, but it was a good occasion to observe people and to talk with them. Also, I could take my time just to sit and let my sight follow a curve after a curve after a curve after a curve...
For there are a lot of people travelling from Potosì to Uyuni, I would suggest to book in advance (at least a few hours), but I felt a bit unconfortable after six hours in my seat looking at some locals who had to stand all the time in the aisle, since there were no seats left. Why didn’t I share my seat with one of them?? Why??
Just in case you are thinking of driving your old Civic around, here is what the "roads" look like and there are NO signs at all. To reach Uyuni, you can take an overnight train but it only leaves on certain days and it does not go all the way through. The bus is another option though I will admit it was one of the worst bus trips we had on our trip. The first bus is pretty good and we saw the most amazing sunset of all our travels from it. We had to change at a reportedly dangerous bus terminal in Oruro but we stuck together as a little group of gringos, some watching the backpacks as the others went and got egg sandwhiches and fries topped with sausages. The bus from Oruro to Uyuni was very cramped so it was hard to get any sleep on it. It was a good thing that Tonito Tours let us sleep in their downtown office upon our arrival at 3 am! On the way back to La Paz, we went to Potosi and from there you can get a more luxurious bus back to La Paz, well worth the diversion as well as money.
There are numerous operators offering tours of the Salar de Uyuni. Tonito is one of the more popular and for good reason, they are dependable and great value. We saw a lot of stranded trucks out there and some crazy drivers too. Our guide got us from one place to the next in dependable if unspectacular fashion. It is a four day/three night tour and includes all your meals, accomodation, and travel through this beautiful but hostile environment. I can't imagine doing it on your own and it would probably be more expensive anyway. The tours are about $80, not bad for four days, huh? You can book it in La Paz at Sargarnaga 189 Office 9 (their local outlet)
You can or visit for a day the border of the salar or do a tour of three or four days travelling through the whole lake, visiting the "laguna verde" and the "laguna colorada" and as well the "isla pescado", all very beautiful places....(all though I haven´t seen them all personally I can say that after watching so much pitures of friends, documental reports in tv and so on. I didn´t have the time to do the long tour unfortunately. Also it´s possible to go through the salt lake and go directly to Chile (don´t have to return to Uyuni).
There are a couple of bus companies making the round to Uyuni from as far away as la Paz, Oruro, and Potosi. The price is dirt cheap at under $1 USD an hour.
Another alternative is to take a train from Oruro to Uyuni. It's slightly more expensive than the bus.
For those of you with less energy, you can hire a taxi to the Patio Sur for a few dollars. Or, just take the taxi over there and walk back to town :).
Lorsqu'on va faire le tour d'uyuni, on peut seulement le faire en jeep. c'est trippant 4 jours a voir plein de paysages, lagunes, volcans, desert....