I promised that I would do a tutorial for flushing the heater core, including pictures, so here it is. First off, I appologize for the terrible pictures; I will try to make up for it in explination. Please keep in mind that this was done on my truck, a 1999, 3.9 v6.
Locate the two coolant lines running into the heater core, which is on the interior side of the firewall. They will be located to the left side of the break booster.
Follow the lines around your engine bay and you will find that one line leads to your water pump, and the other line runs into your intake manifold. The coolant, which is the source of heat for your heater core, runs from the intake manifold, through the heater core, then into your water pump to start the whole process over again. Keep this in mind because you will want to flush in the OPPOSITE direction the first time.
*Note: It will be handy to have a friend to be able to help you, but not necessary.
Locate where the rubber coolant line meets up with the hard line of the water pump. This will be a much more convenient location to flush from. This will get slightly messy so lay something down under your truck, or do this job in a place that you don't give a sh*t about the floor. Loosen the clamp, and slide the hose off of the hard line.
Follow the heater core return hose around the back of the motor, to the left side of the motor. Before it returns into the intake manifold, it meets a coupler. This is located on the hose where it runs between the motor and the stock air box.
Loosen the front clamp and slide off the hose from the coupler.
You are ready to flush! Simply grab a garden hose and hook it up to the hose, running into the heater core, that you just removed from the coupler. I just held it together with my hands, but they sell adapters if you want to waste your money.
Have the earlier mentioned friend turn on the hose and let her rip! To avoid a bigger mess than you already have going, connect a hose to the end that is spewing water all over the place. This way you can aim it into a bucket, or into your neighbor's garage. Let the water run for a couple of minutes.
*Note: The bucket, besides shortening cleanup, will allow you to see any debris that was clogging your heater core.
Simply do the same thing, but in the opposite direction, through the hose that you unhooked on the other side of the motor.
From here, you can simply repeat steps 3 and 4 until you are running completely clear water. When done, reconnect all hoses. Make sure your coolant reservoir is full. Start the truck for 30 seconds, then shut it off. Open your radiator cap, slowly! I don't want to be responsible for coolant in your eyes.
Fill up to the top, and also make sure that your reservoir, once again is full.
You are done! Pat yourself on the back! I just hope you were having a couple of beers while doing this; for your own sake.