Instructions
Invest one point into "Beast Mastery" in the Beast Mastery talent tree. The talent is the tree's 30-point talent, which means you must place 30 points into the Beast Mastery tree before the talent becomes available. You must be at least level 69 before you can learn the talent.
Go to Azuremyst Isle. If you're alliance, the easiest way to reach the zone is by traveling to Darnassus and taking the boat from the right-most dock in Rut'theran Village. If you're horde, fly or water-walk to Rut'theran village from Darkshore and take the boat from the right-most dock.
Travel to Stillpine Hold in northern Azuremyst Isle. Once you reach the area, you'll see a cave entrance. Enter the cave and make your way to the back to find the Kurken.
Left-click on the Kurken to target it and click your "Tame Beast" spell. The Kurken will charge you and attack you while you attempt to tame it. Do not attack it or move and eventually the Kurken will appear under your control.