Here are the sorts of questions you can ask in a long interview.

Sample questions about how people lived and about their family:
-Did you work in the country from which you moved?
-Did you change your job when you came here?
-In what kind of house did you live? What did your room look like?
-What did you like to eat?
-Do you remember when you first fell in love? With whom?
-When/how did you meet Grandma/Grandpa?
-What kind of boy/girl was mom/dad?
-How did you celebrate holidays?
-What holiday do you remember best?
-When (if ever) did your family get together for meals or to celebrate?
-What games did you like to play?

Sample questions for people who moved here from another country:
-Where were you born?
-Why did you move?
-How did you come? Were there any difficulties or anything special that happened?
-What did you feel when you first got here?
-What was you life like during your first years here?
-Who was your best friend? Was s/he Jewish?
-Did you feel "at home" in that country, or did you feel different from others?
-In which school did you study? Did you belong to a youth organization?
-What language did you first speak? Did you know English before you came here? Did -you have trouble learning it?
-What did you enjoy doing most?

For additional ideas and directions, go to "Do I Have a Story for You" in the moadon at http://www.rootsandme.org.il.

You can get general information about what was happening at the time you and your family members were born from these sites:
http://www.historychannel.com
http://www.nytimes.com/learning/general/onthisday/archive.html
http://www.ou.org/about/judaism/bhyom/
The following is very U.S. oriented:
http://www.dmarie.com/timecap/

For very exact information about what happened in the news on days of birth, you'll have to go to your local library and ask for copies of newspapers from the dates you want to see.