The method of flushing largely depends upon the system's current state. If it has not been maintained well or poorly over its previous life, you'll want to do the most aggressive flush you are comfortable doing or able to do, e.g. drain coolant, refill with water and a chemical flush, drive a couple days, drain, fill, drain, fill, until no color in what comes out. Then fill with proper coolant/water mix.
If the system has been well maintained over its previous life, you don't necessarily have to do a flush at all. Just drain the system and refill with proper coolant/water mix.
You say your radiator needs to be replaced, but you don't say why. Is it clogged, leaking, or what?
If it's clogged or doesn't flow properly, you can take that as a sign that the system has been maintained poorly and adjust your maintenance tasks accordingly.