by bus
This is the most common way of traveling to Argentina. There's three bus lines that go there, Geminis, Andesmar, and Pullman Bus. The prices float around 60 USD 30,000 pesos, and all of them leave from San Pedro three times per week. Other choices can be found in Calama, but it might defeat the point a little, since you'll go through San Pedro again, in any case. Going to Uyuni in this way can be done only from Calama; the fares are cheap, though, sometimes as low as 8.000 pesos ~20 USD.
into bolivia
You have to take attention booking with tour operators in Chile, since all the tours in UyuniBolivia have to be guided by Bolivian tour-guides, chilean tour guides are not authorized to conduct tours in the Uyuni salt flat.A handful of agencies offer 3 days/2 nights tours to Uyuni. It does not really matter who you book with, as they mostly join forces at least in low season and fill up their Land Cruisers with people from other agencies. The going price starting at USD 140, March 2011 is some 40% higher here than in Uyuni, even though the itinerary is identical, only reversed. There is the advantage of there usually only being a few Land Cruisers at each site since you see things at different times of day to tours originating in Uyuni, where there can easily be a hundred tourists at each stop. There's also the possibility to return to San Pedro a day later, for a surcharge of USD 20.
Accommodations are quite basic, with frequent lack of hot water and electricity. Meals are filling but hardly gourmet and vegetarians may find themselves a little lacking in protein - bring plenty of snacks as supplies en route are extremely limited. If your tour agency does not provide water, ignore them when they tell you it is easy to buy on the journey-in our experience it was not, and you are better off bringing it all from San Pedro at least 2l per person per day, although at that altitude more would be good.
A sleeping bag and plenty of warm clothing are essentials, it gets very cold at night.
The first night is spent at Laguna Colorada, at 4370m, so it is advisable to spend several nights in San Pedro, to acclimatise before taking the trip. Even then, AMS is a considerable risk-take the usual precautions, and if you have any reason to be particularly worried about altitude consider taking the tour from Bolivia instead, where you will have far more opportunities to acclimatise to high altitude beforehand.
It is essential to get a written itinerary from the agency, specifying all the sights in the order they are to be visited, and also meals and accommodation whether shared or not. Some costs may not be included: Bolivian immigration, entry fees for national parks and museums. Ask about these at the agency.
Read travellor reviews of different agencies at the tourist information office. Estrella del Sur has had a lot of good travellor feedback with excellent guides 140 USD, March 2011. Keep in mind that most guides/drivers do not speak English. Choose your tour company wisely.
by plane
The nearest airport is El Loa CJC, located in Calama. The usual way to fly there is to take a plane from Santiago; there're flights from Antofagasta and Iquique as well, though. Three airlines stop there, and only for national flights: LAN has the most flights, and the best support, but isn't always the cheapest, Sky Airline terrible website, better service than LAN, and PAL. To get to the airport, you have two choices: taking a taxi from Calama about 5,000 pesos, and then a bus to San Pedro 2,500 pesos; or taking the transfer, Licancabur, that charges a fare of 10,000 pesos in regular trips, and 12,000 for "special" trips late at night.