There's an easy way... Let your engine and water pump do all the hard work
Many theories and practices but all involve removing fittings and hoses which can end up in fumbled disasters, especially when it comes to removing the bottom hose and elbow from the radiator itself... Not good...
This simple method avoids all the heartache!
Get the engine up to operating temperature then turn off.
Slowly and carefully open the coolant expansion tank cap, leave it off. Disconnect the thin top return pipe to the expansion tank and force the end of the pipe into a 4 ft length of garden hose and a big enough bucket to catch the waste coolant.
Now put a hose pipe into the filler neck and turn the water on (use a hot water tap, not cold as this would just simply close the thermostat back down limiting the full circulation and attempt at flushing the system thoroughly if you did use cold water)
Turn your heater controls to hot and start the car up... No bleeding, no fuss, as long as the water is circulating and coming out the return pipe into the bucket instead. Once it runs clear its all flushed out... Turn off the hose pipe and turn the engine back off.
Now fresh coolant just poured in while the engine is ticking over again until you start to see the coloured coolant come into the bucket... Depending on engine variant just put the right amount in for a 50/50 split of the solution and fresh water that's all ready in the system. i.e. 6 ltrs total for the cooling system = 3 ltrs of neat coolant
Turn off the engine again. Reconnect the return pipe back to the expansion tank. Leave the cap off and start up again and leave it to tick over watching the level and topping up as needed until the radiator fans have kicked in... Turn off, refit the cap... Job done
Easy when you know how...
Just dispose of the old coolant responsibly at a local council refuse depot