Very carefully:
You have to surprise the bear. Therefore you take a cold bath (to remove most of the "man"-smell) then you find where the bear i question has peed and rub the dirt on yourself - that is called olfactory mimicry. Then you look for the bear. When he slumbers, you carefully approach the bear, very quietly, holding your breath. :biggrin:
When close enough, you exhale your fetid breath and punch him with your left fist in the middle of his snout/nose. When the bear rises his head, you punch the bear on the windpipe - larynx with your right fist and as hard as you can. You have to put all your weight behind that punch or you may suffer the consequences.

If you hit him correctly, then the bear will faint (the so called vagus-reflex, when hard enough, makes the heart go into fibrillation, which is very inefficient in pumping blood and the bear faints almost at once; that is why you never ever should hit a human on the wind pipe).

You now have approximately 1 minute to strangle the bear: since his neck is very thick the only way to do that is to compress the carotid-arteries just approx. 1½ inch to each side of the windpipe. To do that efficiently you push very, very hard with your thumbs where you may feel a very weak heartbeat, which BTW will be very fast and thus quite difficult to feel. It takes approximately 4 - 5 minutes for the bear to go to bear heaven, but his fighting spirit will never revive ... :\
All the above will work if you do it all correctly.
If not ... you'd better be very fast at running and climbing ... or become the bear's next meal. :|
You could be two hunters doing this. You could also use a club to hit the nose. But for the wind pipe hit the club is too clumsy - there the hit must be dead on. For the strangulation you could grab some nut-sized stones instead of using your thumbs, but the risk is that the stones may glide to the side and thus not occlude the arteries. ^_^
This method actually works, when performed correctly. You could practice on bear cubs (when they are half grown and only approx 80 kg), or on sick and old animals, but you have to do it with a good sized and healthy brown bear male to prove your manliness. And you have to have at least two unrelated male human witnesses ... ()
However, when successfull, you will get the choiciest part of the bear's meat, his dried heart, and his claws. After first a cold bath, then at least ½ hours sauna and then cooling down in the snow and brushing your teeth with birch twigs, you will be accompanied to your resting place by at least two blond, blushing, well proportioned, scantily clad young women, who will do their best to keep you awake as long as possible. Therefore I advise you not to drink too much alcohol ... or not to hunt the bears in this way. ()
Edit: @mk: is this post a nef of the highter quality and grade?