After LAB quit flying in 2007, Aerosur and TAM (not to be confused with Brazilian TAM Airlines) are the major airlines within Bolivia, with flighs between most major cities. It is cheap but not always reliable and flights are delayed or suspended sometimes. Cobija, Cochabamba, La Paz, Puerto Suárez, Santa Cruz (El Trompillo and Viru Viru), Sucre, Tarija are the main airports to be served.
There are two train lines in Bolivia which are interesting for travellers, one running from the border with Argentina north to Oruro and one between Santa Cruz and the Brazilian border, sometimes mistakenly called the death train. But that is mostly because of delays and the heath. Over here you can find the most recent time schedule of the north south line between Oruro and the Argentinian border.
The Administradora Boliviana de Carreteras keeps an excellent website that details road conditions in real time: look here. Renting a car is possible, but not necessary or recommended, with roadblocks being just one of the things that will bother you.
Travelling by bus is something most travellers can not avoid. Although buses travel the country frequently between most major towns, roads are not in a good condition except for some parts near La Paz, and roadblocks can be a problem occasionally. That said, you will probably be able to take a bus between two towns within a day. The routes most used by travelers are the La Paz to Tupiza road and side branches to Tarija, Potosi, Sucre and further on to Santa Cruz. Travelling by bus further east and north is possible but takes much longer, especially in the wet season.