By plane
Boliviana de Aviación (http://www.boa.bo) and AeroSur (http://www.aerosur.com) both offer flights from Santa Cruz.
By bus
There are buses going all the way to Rio de Janeiro in Brazil, 28 hours away. Crossing the border to the Brazilian tourist town of Corumbá is easy by taxi. Be sure to note border opening hours, the Brazilian border may close early on Sunday.
By train
There are regular trains going to Santa Cruz from Ferroviaria Oriental. There are 4 services of varying comfort and price. The Ferrobus has Cama Bs. 250 and Semi-Cama Bs. 222 which runs overnight leaving at 18:30 pm on Tuesday, Thursday, and Sunday. The Expresso Oriental costs Bs. 127 and leaves at 4 pm on Monday, Wednesday and Friday. The local service "regional" is not advisable due to longer travel times and greater discomfort. It leaves daily at 11:45 am. The Mixto leaves on Thursdays and costs Bs. 47. The station is quite a ways south of the city center.
Note the station of Puerto Quijarro is closer to the border, if in transit to Brazil.