Depending on the year of the S10 can vary the procedure. But the heater core should be located behind the glove box. Remove the glove box, remove the blower motor and there should be a compartment for the heater core.
Remove the heat/vent module, remove the heater core access cover screws, remove the heater core access cover, and then remove the heater core from the heat/vent module. This is the easiest heater core to replace.
It should be located on the passenger side of the firewall. Start by draining the coolant. Then remove the lines going into it. The remove the cover to access it.
