the blower on my rheems criterion II gas heater does not shut
off how can I find and replace the problem

Older furnaces use a fan center and a limit control. Newer furnaces may have the blower relay on the control board and use a timed shutdown.

If you cannot turn the fan off with the fan on/off control and the tstat is not calling for heat, then it's a pretty safe bet it's the fan relay.

Follow the "bread crumbs". Follow the "money".his In this case it's "follow the blower motor power wires".

Possible defective parts:

Fan relay/furnace board.
limit control
Thermostat
Thermostat wiring

If you reset power to the system what happens? Does the fan come back on immediately, or only when there is a call for heat/cool or you turn the fan on manually?