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:


Dambriūnas, Leonardas; Klimas, Antanas; Schmalstieg, William R. Introduction to Modern Lithuanian Brooklyn, New York: Franciscan Fathers, 1966


Pimsleur.  They only have an introductory course for Lithuanian, but the emphasis is on speaking it conversationally with simple sentences and conversations.

Eurotalk.  Slightly different approach from Pimsleur, they start with some basic vocabulary.

You might also find free short courses for the Lithuanian language on YouTube.