Grandma used the “tie on the needle” method.
I’ll attempt to explain: take a stitch and leave a 3” tail. Repeat stitch. Now you are ready: hold tail with one hand and circle the tail once and come through the loop you just made, bringing loop to a closure by pulling on needle. This completes first half. Hold tail again and with needle, circle tail opposite way from before, bring needle through loop and pull needle until loop closes up securely. Cut thread, leaving a tail equal in length as other tail. Done. In essence, this is a square knot.