How do I repair a burner on an electric stove that is on all the time even if turned off?
I'll bet the control switch is broken.  This is not a difficult fix, but usually requires lifting the range top to access the wiring harness and install a new switch. Most appliance stores with a service department will also sell the parts.  If your range is a new solid state computer controlled, you may have a bad control board. If that is the case, the parts are expensive and should be done by a tech. they are very hard for a consumer to trouble shoot.