What controls the speed of a range hood fan? , only when i push the hi button or the low speed button, the hi speed button only works. its a old model built in 1960 , can't find the model number 42" inch type

You will need to check inside the button contacts to identify if the control of current is by a series resistor or by the coil winding.
Since the high speed is working it is possible that the series resistor coil is open.So check for loss of contact continuity in the switch, if not you can use the present model of electronic fan controllers to give you a variable fan control. This can be connected to the main hi speed connection.
Tip: Identify the wattage and buy the regulator according to the specs.(42 inch type)

I have similar problem fan works at Lower speed buy keeps running at same speed when changed to higher speed on regulator