In a nutshell, very carefully. Remove the clamps and split the hoses with a knife where the hose is on the outlet tubes. Take some spray lubricant and spray some on the connections while you force a screwdriver around the hose. That will keep you from damaging the outlet tubes. I hope you are not replacing the heater core as it is a very large chore.
This isn't going to be easy unless you have the smaller size 'Vulcan" engine - in which case you might actually be able to get your hands down behind the engine.
Couple of thoughts:
On the firewall behind the intake. PITA to get to or even see for that matter
take heater hoses off the firewall heater box and unbolt heater box on the firewall and then pull heater box down from under the dash and you will see the heater core inside, replace it in the box and bolt everything back together.
How much will it cost me to replace the heater core in my 1999 Mercury
If its just the cord, then follow the old cord to the back side of the engine ( really the side of the engine closest to the firewall ) and replace it. When the engine is cold, plug it in and you will hear the block heater heating up. If you don't hear anything, then replace the heater also. That requires a little more knowledge.
What you have to do, is replace the heater core itself
heater core has a leak replace heater core
Near the firewall behind the engine, or under the dash near the heater core.
LOTS - it is virtually inaccessible .
The AC has to be dischared, and the AC lines have to be removed at the firewall. The AC drier has to be remved, because there are nuts on the outside of the firewall under the hood to remove that are hidden by the drier. I believe there are 4 nuts to remove, but there might only be three.
They (2) should be up by the firewall on the passenger side
the heater blower resistor is located on the passenger side footwell near the firewall. a complete how-to replace the resistor, along with photos is available on newcougar.org http://www.newcougar.org/forums/how-tos/3732-fixing-heater-blower-resistor-install-photos.html
Cut off the crimp connectors, pull the old hose off and replace with conventional heater hose and conventional hose clamps