In general, your best bet would most likely be to search for state and local (county/city) records. Try public libraries, halls of records, historical societies, etc. If the school he/she taught at still exists, they might even have records of your family member.
If you can provide more information (e.g. location, dates), we might be able to offer more specific advice, too.
Best of luck with your search!
Thank you for responding. I found her on a:
1900 Census dated June 15 1900 Chelmsford, Middlesex, MA
Head Minnie A Worden 36 (D.O.B. July 1864) Single Teacher
(her Mom) Dorotha C Worden 61(D.O.B. Nov 1839 Widow
So, Dorotha is my Mothers Mother. My Mother was Christine Dorothy (Lapham) Moore. Her Mother was Pauline Willoughby (Worden) Lapham daughter of Dorotha C (Pearson) Worden and Charles Worden. In my mothers things I found a photo
This is the photo and I am trying to find out who it is?
As far as I know my mothers family lived in and or near 31 Littleton RD in Chelmsford MA for a very long time.
951 850 1684
If I understand correctly, you are looking for potential names of family members who are in a photograph that you found among your mother's things. Since you believe that the family lived in the same location for a long time, you might look at census records from other decades to see if more names/relatives are listed for the household.
Additionally, when I looked at the 1900 census record you mentioned (Person Details for Minnie A Worden, "United States Census, 1900" — FamilySearch.org), I noticed that Doratha C. Wordon was born in Norway. The National Archives' immigration records and naturalization records might contain some information about your ancestors. You can find information about researching these records here:
Beyond that, you might be able to find birth and death records, marriage records, property records, etc. at the state, county, or city level (e.g. halls of records, county clerks, public libraries). The website of the Chelmsford Historical Society, for example, has some information about researching local family history: Chelmsford Historical Society - Genealogy. Massachusetts also has a Registry of Vital Records and a State Archives that could prove helpful: Archives: Researching Your Family's History at the Massachusetts Archives.
It's unlikely that NARA will have any records of a family member unless they had some kind of interaction with the government concerning the courts, land, or certain kinds of employment such as military service. NARA is the repository of national government records created by government agencies. NARA rarely has specific information about individuals unless they worked for government and even more rarely does it have pictures. If you don't think the family member had any business with the government, you may want to try a local or state historical society/archive. Sometimes schools have archives or small heritage societies as well. To help find other possible sources please ask yourself these questions:
Is he or she still alive?
If not, where and when did they die?
Where have they lived?
Where did they work?
Were they in the armed forces?
If yes to the above, what unit did they serve in?