The best way to fix a heater core leak may be to simply replace the part with a new unit. There are products that can be added to the cooling system to temporarily plug leaks, but they may end up clogging coolant ports and radiator tubes as well. It may also be possible to have your existing heater core repaired after it has been removed. This is often more expensive than simply purchasing a new unit, though in certain circumstances it may be the only option. It is also recommended to verify that your leak is actually what it appears to be, as a number of different things can appear at first to be a leaking heater core.
Before going through the work of removing a heater core for replacement or repair, it may be a good idea to make sure you have a heater core leak at all. If you notice water on the ground underneath your car, it isn't necessarily coolant. It may simply be condensation from your air conditioning system, which in some cases can collect in the heater box and then drip out from the same place as a heater core leak. If you collect the drippings, it should be possible to determine if it coolant or water. Otherwise, the cooling system can usually be pressure tested to tell for certain.
In most cases, the first step to repairing a leaking heater core will be to determine the location of the component within your vehicle. Heater cores are typically located inside a plastic or metal heater box that can be inside either the passenger or engine compartments. Most cars will locate the heater box under the dash, and other vehicles may have it in the engine compartment. The easiest way to locate it is to find the heater hoses and follow them. A vehicle will typically have an inlet hose and an outlet hose, both of which connect to the heater box.
Once the heater box has been located, the rest of the process can be quite complicated. Some vehicles have a panel under the dashboard that the heater core can be removed through, and others will require you to remove the entire dash. If the heater box is in the engine compartment, it may just be a matter of opening the box, or the heater core may need to be removed from inside the vehicle.
If replacing your heater core with a new unit is not an option, repairing it may be possible. This process typically involves boiling the core in a large tank for several hours, passing a rod through the tubes to clear them of blockage, and then soldering the tubes wherever a heater core leak has developed. Copper heater cores can usually be repaired in this manner, but aluminum cores typically can not. This is usually the recommended method of repair, since additives designed to plug leaks from the inside can cause blockages elsewhere in the system and lead to overheating.