This is a traditional fold for a flat diaper, likely your great-grandmother used a fold like this with pins and a wool diaper cover. Flat diapers are a little more difficult to use, but they are fast to wash and dry, cheap to buy and they fit from birth to potty-training. That is a lot to say for a simple square of cloth.
Start with the diaper laid out flat in front of you with one corner towards you (like a baseball diamond!).
Fold the top corner of the diaper down to form the waist portion of the diaper.
Fold one side of the diaper in towards the middle.
Fold the opposite side in towards the middle.
Fold the bottom corner up to make the diaper the right length for the baby.
Fold each side in again to make the diaper narrow enough to fit between baby's legs.
Place the baby on the diaper and fold the front edge up between baby's legs. Fold the front edge down if needed. Fold each of the back edges in towards the front. Secure with pins.