To have access to Brawler’s Guild, you need to purchase this item: “Blood-Soaked Invitation”. The item can be bought from Black Market Auction House in “Tavern in the Mists”.
The price starts from 1k gold (BID) and goes up depending on the population of your realm. If you are on a high populated realm, expect to pay more as there will be more players interested to buy the item. They will bid and the price will go up.
The good thing is that there are usually 10 “Blood-Soaked Invitations” all the time and in a week, you could pay less as everyone should have gotten the item by now.
Brawler’s Guild was introduced in the recent 5.1.0 patch, it is some sort of PVE arena where a player will have to fight and defeat different mobs.
#update.
The item also drops from some mobs in Krasarang Wilds. Check this wowhead page, the comments.
Update 2
I’ve read on a forum that the spawn time for the rare mobs is randomly between 35 minutes and 1 hour.
The drop chance is around 2.5% (extremely low).
The Black Market AH prices are getting lower but the invitations are still expensive, at least 30k gold on medium populated realms.
Most of the players hate the system. It’s really unfair to ask for such high amounts of gold or to put just 2.5% drop chance.