I'm just gonna come out and say it: A leaking heater core sucks. One of the symptoms of a leaking heater core is wet carpet on the passenger side of the vehicle where the heater core is most often located. Another common symptom is that the windshield fogs up when you use the defroster. It might even leave an oily film on the windshield and smell like coolant when you activate the defroster.
If you have these symptoms, you likely have a leaking heater core. The repair of this can run the gamut from very easy to OMG I want to shoot myself. The easy ones are normally accessible from the engine compartment. The difficult ones are located inside the dash and you need to remove the dash and the HVAC system in order to access them. As if that isn't difficult enough, you will also need to evacuate the AC system because you'll be disconnecting the evaporator when you remove the HVAC unit.
Before you say “stop-leak,” remember the above paragraph. One temporary fix I've done a few times is to bypass the heater core altogether if it's leaking. You can do this by routing the inlet heater hose to the outlet. Just disconnect the heater hoses from the heater core and either join them together or rout one back to the engine. This creates a loop for the coolant to flow back to the engine. Your engine won't know the difference; the heater core is just there for your comfort and doesn't affect engine performance at all. You can run it like this for as long as you like. This way you don't have to deal with that leaking heater core right away.