Along with Latvian (Lettish) and the now extinct Old Prussian, Lithuanian belongs to the Baltic branch of the Indo-European family of languages. Lithuanian is often said to be the most conservative living Indo-European language, retaining many features of Proto-Indo-European now lost in other Indo-European languages.
References for learning to speak Lithuanian:
TEXTBOOK:
Dambriūnas, Leonardas; Klimas, Antanas; Schmalstieg, William R. Introduction to Modern Lithuanian Brooklyn, New York: Franciscan Fathers, 1966
ONLINE:
Pimsleur. They only have an introductory course for Lithuanian, but the emphasis is on speaking it conversationally with simple sentences and conversations.
http://offers.pimsleur.com/
Eurotalk. Slightly different approach from Pimsleur, they start with some basic vocabulary.
http://eurotalk.com/us/
You might also find free short courses for the Lithuanian language on YouTube.