Raw water or coolant?
If it's the raw water, the process is relatively straightforward. If you have a raw water flush kit installed in your raw water supply, like Groco sells, it's a snap. If you don't, it's a little more involved, but still easy.
You'll need a five or ten gallon bucket filled with fresh water, and access to a dock hose. First, close the seacock on the raw water intake, underneath the platform in the port lazarette. Then, (if you have the raw water flush kit) close the valve on the kit, take out the plug, attach the service adaptor, attach a short hose to the service adaptor, then put the end of the hose into the bucket (which is filled with water).
If you don't have the raw water kit, you need to take off the hose feeding the raw water pump, and replace it with a short hose of the same diameter (the end of which goes into the bucket of water). Make sure to use a thick-walled or reinforced hose, as it will be a suction hose, and if it's too thin, it will collapse.
Some advocate attaching a dockside hose directly to the intake - big mistake, in my book, as the pump is there to suck in water. If water is forced in under pressure, it could result in damage to the rubber vanes on the impeller. Then you'll get bits of impeller blocking or impeding the flow of raw water further downstream.
When I do this, I have the bucket of water in the cockpit, with the hose leading down to the engine. Prior to starting the engine, I fill the hose up with water using a funnel - this is to minimize the "run dry" time of the impeller. Also, having the bucket in the cockpit allows me to kill the engine quickly if something goes wrong. I can also fill up the bucket with a dockside hose, replenishing the bucket water.
Run the engine for 10 to 15 minutes (filling the bucket as necessary). When done, kill the engine, re-connect the raw water intake hose, and re-open the sea-cock.
There are some acidic cleaning fluids that can be used to clean out the innards of the cooling system, wherein you run the engine for a short period of time to get the fluids in, then turn off the engine and let them sit for a while before flushing out with clean water (maybe a few hours? I never use the stuff, as it's toxic, and you need to re-route the exhaust if the boat is in the water). Also, on an old heat exchange, the acidic stuff could eat away at the already corroded tubing, leading to a leak between the raw water and the coolant. Not good!
If you're talking about flushing coolant system... I've never done that, but any mechanic would be able to do it for you. Since it's a closed system, there shouldn't be any corrosion or marine sediments. If there are, you've got a leak between the two systems, somewhere in the heat exchange unit.