It depends how dirty your cooling system is. If it's overheating and the radiator is extremely plugged with scale, I would consider replacing it. Adding a strong acid to your cooling system will cause damage to it and you may end up with a radiator that cools, but also require a lot of new and expensive parts. Looking inside your rad will tell you a bit about the health of the cooling system. You could also remove the upper rad hose and look inside the engine.
If it's fairly clean inside then I would consider just flushing it with water, or an off the shelf cleaner or flush chemical. There may be a slight film of oxidized looking material. This is not uncommon especially if you had silicates in your coolant. Many manufacturers are getting away from silicates these days. But if you had it in the system, they form a layer over the metals to protect them from corrosion. This isn't a big deal.
If you need to flush because the system is really dirty, I would drain the entire system, add a flush T fitting on one of the lines to the heater core, flush out everything with plenty of clean water - only if you have soft water in your area - never use hard water. A flush T looks like this:
It's installed on a heater core so that it blows everything out of the heater core, and through the engine backwards from the normal flow of coolant, basically flushing any [censored] out.
You could then add Prestone Engine
Cleaner (not flush) which is designed to be left in your system for several days. Depending on the size of your system and how dirty it is, maybe add 2 bottles. BG and some other companies make similar products.
You could also add a bottle or 2 of Prestone
Flush, depending on your cooling system's capacity. This is designed only to be left in your system for
10 minutes as it is mildly acidic (far less so than Cascade) anything longer and there's a risk that it will begin to erode your cooling system and engine. I would add this and run the engine at fast idle or drive around the block, until the thermostat opens. Once it is fully open and coolant in the radiator (and the flush) is being circulated through the engine and heater core, go 10 minutes, stop and drain.
After any cleaning agents, you need to flush the system with clean water, tons of clean water to ensure all the acidic agents are gone. The flush T is really the only way to do this, other than disconnecting a heater core line and inserting a garden hose into it. I let the water run for about 15 minutes and even start the engine to ensure there's circulation of fresh water and no air pockets.
It's critical that anytime you add water, particularly through a flush T, into your engine, that the engine be COLD. That doesn't mean the gauge says it's near the letter C on the dashboard. It means put your hand on the engine an it should be ambient temperature, maybe slightly luke warm. If the engine is hot, or even partially warmed up and you blast cold water through it, you're very likely to crack or warp something.
Finally, drain as much water as possible from the system and add the correct amount of concentrated coolant. For example, if the system is 7.5 liters, I add a 3.78 liter (4 quart) bottle of coolant. This gives me a little more than 50/50, which is the right amount in most applications. You need to get all of the coolant into system to ensure the correct mix. Then, add water to top it off. The capacity includes the overflow bottle, so I save a little coolant to add to the overflow with water. If yours is a sealed system with a pressurized overflow bottle, this isn't required.
If you want to use pre-mix coolant, you will need to get ALL of the water out of the system before adding the pre-mix, otherwise you're diluting it below the intended ratio of coolant/water. This means blowing water out of your heater core, opening all the engine block drain plugs, the drain at the bottom of the radiator, all the hoses etc. It can be fairly tricky to get everything out - which is why I find the concentrated coolant a better method. I'm sure that my block wont freeze (and crack) and I have enough coolant to protect against corrosion.
Some people get quite OCD about using distilled water. If you have soft water coming from your hose then using it isn't a big deal. Any shop you take the car to is using that water to flush.... so.... You could add distilled water for the final fill but I don't worry about it since my water is very soft. If you have hard water with a lot of mineral content, DON'T use it to flush or for the final fill.
Make sure you use the right coolant, which there is 100's of threads and arguments on. But in short, be sure what your car takes - whether it can have silicates, phosphates, is an OAT, HOAT, P-OAT, 2-EHA etc. The color of the coolant is only a dye and does not actually indicate anything about the coolant type.