I have little experience in tracing Fijian Indian ancestors but in the main it is the same as for any other ancestors. Start with what you know about your parents and grandparents, and work backwards up the tree with birth, death and marriage registrations found through the indexes, all on microfilm from the Family History Library (FamilySearch). See How do I trace my family tree. Use an ancestor chart to help you keep everything straight, or use a family tree program, or even an Ancestry family tree.
If you are in Fiji you can go to a Family History Library or the National Archives and access the films directly, but outside of Fiji you have to hire the films and wait for them to arrive.
Indian records come under the ‘General’ category where they are not in a separate category for Indians.
The Family History Library also has immigration-related records of Indians, and the National Archives would have those as well. Here is an example of the civil registration (of births, deaths and marriages) records held by the Family History Library for Fiji:
You can see that in some entries Indians are recorded separately, and others are ‘general’, which means ‘non-Fijian’.
Eventually you will get back to someone who was born in India, and then you can start looking for records specific to Indian immigrants. Search the FamilySearch catalog. Here is the entries under ‘Emigration and Immigration’:
