Hi Robert,
There is little anyone can do to help you without alot more information than just your name and country.
If you know the full proper name of some of your ancestors (ones born before 1930), a rough idea where they lived (i.e. a city or town) and a year (or even decade) of birth as accurately as possible that can be very helpful to getting started. As a generalization only your family will be able to help with information on people born after 1930 as those records are still private.
While I cannot give a personal recommendation for the website http://jamaicanfamilysearch.com I would say that it appears to give a good overview of some sources that are available as well as some of the challenges with researching Jamaican ancestry.
Another option is to pay for the Registrar General's Department to do the research for you. They charge JMD$850 or USD$10 per hour. You can find more information on their services here: http://www.rgd.gov.jm/products-and-service/genealogical-research
