1. LOCATION is crucial when searching for civil or church records. Be aware of the terminology "ciudad" (city), "municipio" (municipality), "provincia" (province.) Sometimes the capital city of a province and the province carry the same name. For example: the city of Pinar del Rio versus the province of Pinar del Rio. Although Cuba is a small island, you need more information that just the island name to find your ancestor's record.
2. There were 6 original provinces in Cuba until 1978. Currently there are 15 provinces. Find a map of the area you are researching in (with the current province as well as the province in the time period you are researching.)
3. You can acquire records from Cuba, especially church records, by writing directly to the ancestral parish. Records have been centralized in the corresponding province Archdioceses. CubaGenWeb has a directory of parishes and their contact information. (http://www.cubagenweb.org/phones/index.htm) You can also Google the name of the parish and location to get contact information. Please be aware that not all parishes have a full-time priest or the resources needed to provide services.
4. When you examine the documents take advantage of the fact that Cuban church records are patterned on the Spanish model and often will mention not only the parents but the grandparents as well. Often these records include information as to where each of the ancestors was born, whether and where they were living at the time of the event, and sometimes even their occupation.
5. Be familiar with terminology found on records. The FamilySearch Wiki has a Spanish Genealogical Word List that can be of assistance.
6. Civil records are often incomplete and very difficult to acquire.