Find out about their childhood, how they met, married, worked, immigrated, did in the war, etc. This is the most fun part and will give you clues to how to find more information. Don't be too narrow in your search. Include all possible relatives as you great-grandparents' cousin may lead you to the families place of origin in Europe. Get copies made of key photos.
People are always so afraid of loosing a photo.
It took me 15 years to find out my dad's cousin actually had a photo of my great grandparents taken in 1895 but he was afraid of loosing it. I got a copy made and enhanced and distributed dozens of copies. It took us four hours to label and organize all the photos and by then I had the family history back to 1835, with the key fact that all the males came from one town in the hills of Slovania. That person passed away shortly after that evening session, and all that information would have been lost if I had not talked my cousin into spending four hours doing this. Get copies of all old documents held by your family and translations of those in a different language.