Since so much is similar between our modern observation of Thanksgiving, and the celebration of Thanksgiving in Greenbelt, MD during the late 1930s and 1940s, little stands to differentiate between the Greenbelt observation and our modern observation.
Thanksgiving remains today, as it was in 1930s/1940s Greenbelt, primarily a family holiday. It was a time for sharing and introspection (Neville). It was not a time for town celebrations or festivals. Rather, it was a time to spend with one's loved ones and family, giving thanks for what each person had been blessed with.
Thanksgiving was a family holiday celebrated in what we would recognize as the modern fashion--with turkey, cranberry sauce, sweet potatos, squash, and mincemeat and pumpkin pies (Neville). As on any other holiday, the better silverware and better table clothes would have been used (Neville). The meal would have had a more formal atmosphere since the main meal would have been served earlier in the day--perhaps around mid to late afternoon (Neville).
Visit The History of Thanksgiving to learn how the holiday originated.