The best way to find out one's school district is to consult an online search engine that uses geographical identifiers to determine the school district. The U.S. Department of Education's National Center for Educational Statistics provides one such tool, and Great Schools provides a similar one.
Once one has determined the correct school district, it is sometimes still necessary to figure out to which school one is assigned. This can be done by calling the local school district. Many larger school districts, including the Los Angeles and New York districts, provide online search tools which use the requester's home address to determine the assigned school.