If you follow the official "factory-recommended" or whatever steps, you're supposed to also open up the drain bolt on the engine block. If you do that though, you need to torque it down properly and use liquid gasket on the threads when you're done.
I skip that step myself but the rest is exactly as my manual says to do it (both owners and repair).

Before you start make sure the heat slider or dial is all the way on hot.

With the engine cool, drain the coolant (draincock at bottom of rad.) into a bucket and discard of appropriately.
Replace draincock and fill the radiator with water (filtered is preferred but tap is fine) until full, then run the engine until either the cooling fan has come on or it's been blowing heat out the vents for a while.

Drain rad. again and either repeat the previous step or move on to adding the 50/50 mix of antifreeze and water (filtered/distilled/demineralized water is strongly preferred) until the rad. is full. If your engine has a bleed bolt, you should loosen it and keep adding coolant until a steady, bubble-free stream comes out before re-tightening the bleed bolt.

Next, with the rad. filled to the top, you replace the cap but only turn it to the first stop, not all the way closed. Run the engine like this until the radiator fan turns on at least twice. This may not ever happen if you are running your interior fan.

Next you remove the cap again and fill the rad. back up to the top. Replace the cap and tighten it all the way.

Lastly, remove the overflow bottle from the car, rinse it out, and fill it to the max line with the 50/50 coolant mix.

After you've taken the car on an actual drive, check the level in the overflow bottle and add coolant up to the max line.

With this method, whether you "flush" (not a true flush) with water once or several times, the mix of antifreeze and water won't be perfectly 50/50. It will be more like 40/60. That will probably be good enough in most cases, but if you want extra cold weather and corrosion protection, you have some options.
The two that I've used are: either buy filtered water and pure antifreeze separately (not pre-mixed) and add a little more antifreeze than water when you finally refill the radiator, or you could drain the rad. of coolant an extra time after it's been run through the system for a while and refill with pre-mixed (this will bring it close to a 50/50 mix).

P.S. If you spill coolant, even if mixed w/ water, on any painted area, you need to rinse it off with water relatively quickly. Best to keep an extra jug of water by the car in case this happens.
You will need to use a funnel at some point and it makes it much easier so pick one up if you don't already have one.
Finally, antifreeze is toxic and it's best to avoid getting it on your skin etc. If you read the directions on the container, it will say to wear gloves as well as eye potection, and wash any exposed skin.