To get to the Stratholme pet battle dungeon, simply visit Radek Fuselock in Dazar'alor, located next to Happy Holaua as Horde, or Tizzy Gearjolt in Hook Point, Boralus Harbour next to Dana Pull as Alliance. Each will give you a quest, Restless Dead/ Restless Dead, sending you to Sean Wilkers, who is outside the instance portal for Stratholme (Service Entrance, marked as Eastwall Gate on the map). You will then get a quest, Tiny Terrors of Stratholme, to complete the Stratholme pet battle dungeon, and rewards you with Ultimate Battle-Training Stone and unlocks Manapoof Link: Stratholme, allowing you to teleport to Stratholme from Manapoof, located next to either quest giver in your factions capital city, or Dalaran.
This dungeon has two separate difficulties:
Normal
You can heal or revive your pets any time
You must have at least one pet leveled to 25 to unlock
You can only do this once
Access to Postmaster Malown
Challenge
You cannot heal or revive your pets with Battle Pet Bandage or Revive Battle Pets at any time
You must have at least 15 pets leveled to 25 to unlock
Have finished the normal difficulty of the Stratholme pet battle dungeon
This can be done weekly, and rewards Cleansed Remains upon completion
Also has the chance to spawn the optional world quest, which awards an extra Cleansed Remains
Access to Postmaster Malown
Here you can buy Pet Battle Challenge: Stratholme for EU or US Servers.
You'll get guide for completing Pet Battle Challenge: Stratholme