Cuban Family History Resources
Cuba Immigration and Emigration
Brigham Young University's Center for Family History and Genealogy is working on a project called Immigrant Ancestors Project (IAP), their website is: http://immigrants.byu.edu The site focuses on identifying emigration records from European countries of people that emigrated to the Americas (including the Caribbean). Under the supervision of professors and other researchers, students travel to Europe to identify emigration records. Contracts/agreements are made with the archives and the records are digitized. After the records are acquired students extract the important genealogical information and it is entered into a searchable database (free of course). Users of the site can then write to the archive where the record was acquired and ask for a copy of the original record.
Online Cuban Resources
There are some online records for Cuba, but mainly for slaves and/or those that have African heritage. Some of your ancestors might fall into this category. The link to these online records is: http://lib11.library.vanderbilt.edu/diglib/esss.pl
Letter Writing Guide
Letters can be written to local parish archives asking that records be searched you. Requests should be kept short (to one person or family at a time), and donations to the parish can be helpful. The Spanish Letter Writing Guide is very helpful to compose your letters, please remember to write in Spanish.
Resources at the Family History Library
The Family HIstory Library has some indexes of parish records of some Cuban parishes, as well as some finding aids. You can find these through the FHLC.