Hanging (full suspension)
Effective since ancient times, as a method of suicide and execution.
You only need a rope, a chair and a somewhat elevated and strong place that can support your weight.
Tying knots is easy, just watch a YouTube video. I got them right on the first try and I'm not very skilled at all.
You just have to endure pain for 10/15 seconds until you become unconscious. Then you just have to wait for death to take you. In an hour it will all be over.
You must be totally determined, there is no turning back. That is why many do not choose this method.
There are plenty of videos that prove its effectiveness. If you use the image search engine you will see a lot of people who have done it, with various materials and in various places, some of them look too improvised and with little knowledge and yet they managed to kill themselves. I also know two people in my city who used this method to take their own lives.
And about brain damage, you need to be alone without anyone interfering to help you. Once you are hung with the rope tightening around your neck you will simply die. That is why, as I mentioned, it is for determined people, without fear and who can bear a little pain for a couple of seconds.
I don't think it's a brutal method. It's nice, I'd like to see my small and skinny body "dancing" on the rope, like a marionette, until death comes to get me.