It takes roughly 8-9 landed blows to knock someone out.
Be warned that as soon as you start fighting with one person, their friends will all jump in too. Try to pick out lone patrons to pick a fight with, but when out numbered just remember you can either try to bottleneck the group so that only one member is in range (behind the bar can work, as can corners and staircases at times), or kill the friends, as only one knock out is needed to tick off a saloon.
Another issue players might have is with patrons not looking for a fight. As soon as you hit them, they will attempt to run, and if you don't knock them out before they get out of the saloon, it doesn't count. If everyone in the saloon runs, leaving the place empty, just go outside and pick a fight, bringing the fight back inside. Characters aggressive to Marston will follow him when engaged in a fight, and as long as the knock out occurs inside the saloon, it counts.
Although fairly easy to knock out someone, if they start blocking, they are going to keep blocking until they see an opening. If your target starts blocking your punches, block until they throw one, then continue beating them up.
After equipping your fists in the weapon selection screen and readying your fists with LT, you can punch with RT, block by holding RB, or dodge in any direction by pressing X and moving in the direction.
There are 7 towns with saloons in them, and not all of them will be accessible until you have competed the second chapter.
In New Austin:
In Nuevo Paraiso:
In West Elizabeth
If you knock someone out, and consequently die, you lose that check, so as soon as you knock someone out, try to save (sleep) or quick-save (completing a random encounter, using a horse deed, etc.)