Connect hoses to both ends of the heater core sticking out of the fire wall. Direct the other end of one hose toward the ground or a bucket. On the other hose force some water in with a garden hose. If water easily comes flowing out of the hose toward the ground or bucket, the heater core is not clogged. If heater core leakage is a concern block the hose going to ground/ bucket and gently pressurize the other hose with water. Look for water dribbling out of the drain hose that connects to the black box that the heater core is in (if the car was equipped with AC). If no water comes out the drain the core probably doesn't have a leak. Cars without AC may have a drain hose also, but I don't know if they do. Other members might.
Another way to check for leakage is to point both open hose ends upward at the same height and fill with water until both a full making sure all the air bubbles out. See if the water level stays constant. If constant, not likely a leaky heater core. If the the level drops in one or the other after a while, it probably is a leaky core.
After thinking about this more, it is probably simpler to just connect one hose to the core, and blow into it like trying to blow up a balloon and see if air readily passes though the core. If it doesn't, clogged core. If it does, next block the end of the heater core without the hose with your thumb and blow again. If you can't blow air in, no leaks. If you can keep blowing air in, leaky core.
I know how I would do it, but I have all kinds of pipe fittings, adapters, barbed hose fittings, and valve stems connected to pipe fittings. I would adapt and connect a valve stem to one heater hose, and plug the other one, pressurize the core to 15 psi and see if it holds pressure. If it does remove the plug and blow air through the core at no more than 15 psi to make sure the core isn't plugged.
They make products and tools to flush your heater core. The simple version is a hose barb to connect your heater core hose to your garden hose. Then another length of hose to direct the water coming back out to somewhere other than under your hood. Run like that to flush all the air out of the heater core and hoses. Then cap the second hose and your system will get the full line pressure, between 40-80PSI.
If you want more control over the pressure, look up a hydrostatic test pump. It is literally designed to pump water into something to pressurize it so you can test for leaks. They cost about 5x as much as a hose with an adapter barb, but you gain a lot more fine grained control and a pressure gauge.