Once you have identified the town in the Palermo province from which your family originated, it is time to get down to records business. ItalyGenWeb hosts an informative page about the types of records available in Italy. Researchers in Southern Italy are particularly lucky in that records for Sicilian towns tend to be very uniform in content, easy to read, and often span back to 1809-1820, at least forty years earlier than other spots in Italy.
The best bridge into researching foreign records are the records made available through microfilms stored at the Family History Library. Ordered through your local Family History Library, these microfilms obviate the hassle of having to write to Italy for copies of basic vital records. The library has collections which include microfilmed civil and church records from throughout the Palermo Province. Check the Towns and Municipalities page on this site for links to LDS materials.
Another option is to look on- and off-line for transcriptions of records created by other researchers. While these transcriptions should never replace the acquisition of copies of original records, they can be a great starting point. Check the Towns and Municipalities page on this site for links to on-line databases and transcriptions. You can also check the rootsweb.com Italian Records database.
Once you have exhausted information available state-side, it is time to begin accessing records from Italy. About.com has a good Italian Genealogy 101 guide to the names and types of records in Italy. Most Italian records reside in one of two places, the local Ufficio di Stato Civile and the provincial Archivio di Stato. Other records are found in the Uffici di Anagrafe and the local Catholic church parishes.
Brief overview of vital records available and where to write:
Vital Statistics, <1860
order from the Archivio di Stato
Vital Statistics, 1860-now
order from the Ufficio di Stato Civile. Note that privacy laws apply to contemporary records.
Keep in mind that what can not be found in the civil archives may be found in parish records, as the Catholic Church was very active in documenting baptisms, marriages and deaths. However, many records have suffered as a result of being kept in local parishes, so despite the fact that the time period of record-keeping is long, many records have been lost and may no longer exist.