Generally you get records of birth, death, marriage, divorce and other vital records from the relevant agency in the state where the birth, death, marriage or divorce took place. For specific instructions, including information on what to do when these events happened abroad or in unusual places (e.g., on a ship), check out the National Center for Health Statistics' Where to Write for Vital Records. Note: "Where to Write for Vital Records" is also published in The Lawyer's Almanac and the American Jurisprudence 2nd Desk Book.
Birth: Vitalsearch, Ancestry.com and Archives.com have birth records, and the other databases mentioned below might as well. You can order a birth certificate on on expedited bases through www.officialtraveldocuments.com. For specific instructions on how to order official birth certificates from the relevant government agency, see the National Center for Health Statistics' Where to Write for Vital Records.
Marriage and divorce records are available for selected states through Accurint, Ancestry.com, KnowX, Vitalsearch, Archives.com, Lexis and Westlaw.
For more resources, see Jennifer L. McMahan's, "More Nancy Drew than Marian the Librarian: Hunting for Vital Records Online," 53(4) Law Library Lights 8 (Summer 2010). See also the Guide entries for individual states and cities.
Death Records: The Social Security Death Index lists people who were receiving Social Security when they passed beyond this veil of tears. The Index is avaialbe through Ancestry.com.
TLO, KnowX.com and Accurint have national death records data bases. Lexis, Archives.com and Vitalsearch have death record databases for several states. These database also cover people who were not receiving Social Security when they died.
Another approach: Try to find an obituary. Obits could are most likely to appear in a newspaper for the person's last residence or hometown. If the person was notable in his or her field, an obit may also appear in a in a trade journal or newspaper. Of course obits for celebrities appear in general circulation newspapers. (Sources for obits are discussed in the "Obituaries" entry.)
The Online Searchable Death Indexes & Records provides links to state databases, online obituaries, cemetary records, etc.
For more resources, see Jennifer L. McMahan's, "More Nancy Drew than Marian the Librarian: Hunting for Vital Records Online," 53(4) Law Library Lights 8 (Summer 2010).
If that still doesn't do it, and you have some time, you can contact the relevant government agency (as discussed above) to get a copy of the person's death certificate.
England and Wales: English and Welsh birth, death and marriage records are available from FindMyPast.co.uk.