The old knob pulled off easily. Its stem had broken. Examine the new control knob. Its stem has a protrusion on it which fits into the grove on the shaft of the oven's function-control switch. (It would be the same for the temperature-control switch, also.) The new knob slips on easily when properly aligned. You may want to use some gunk from a breakfast cereal box (the clear gummy gunk that is used to hold two cereal boxes together, when sold as a pair) to help the new knob stay on. Using whiteout or paint, mark the end of the ridge on the knob that points to the switch position, so that you can easily tell which way it's pointing.
Was waiting on my friend's boyfriend who is a contractor to switch this knob out but figured it out myself. It just slides on and off with no tools. I am so proud of myself for completing the repair all by myself on my 37 year old oven. My other knob just cracked and I was afraid the inside of the knob was damaged but it is not. Working like a charm now.