Once you’ve done this, head to your local Battle Trainer in your capital city for the starting quest. For Horde, talk to Gentle San located at the top of the Shrine of Two Moons. For Alliance, talk to Sara Finkleswitch in the Shrine of Seven Stars.
All four Spirits will have level 25 Legendary pets including the corresponding spirit reward as part of the team. For strategies, check out my video links for each spirit below.
Whispering Pandaren Spirit <Grand Master Pet Tamer>
Location: Exclamation Point, The Jade Forest (in the middle of Tigers’ Wood on a peak) – 28, 35
Pets: Pandaren Air Spirit (Elemental), Dusty (Flying) and Whispertail (Dragonkin)
Thundering Pandaren Spirit <Grand Master Pet Tamer>
Location: in the mountains above the Shrine of the Two Moons, Vale of Endless Blossoms – 67, 14
Pets: Pandaren Earth Spirit (Elemental), Sludgy (Magic) and Darnak the Tunneler (Beast)
Burning Pandaren Spirit <Grand Master Pet Tamer>
Location: northern end of The Underbough, Townlong Steppes – 57, 42
Pets: Pandaren Fire Spirit (Elemental), Crimson (Dragonkin) and Glowy (Flying)
Flowing Pandaren Spirit <Grand Master Pet Tamer>
Location: Lonesome Cove, Dread Wastes – 61, 87
Pets: Pandaren Water Spirit (Elemental), Marley (Aquatic) and Tiptoe (Critter)
Defeating all four rewards you with one of the elemental spirits as a reward and the achievement Pandaren Spirit Tamer.
You will then be able to do it again as an account-wide daily, giving you a chance to get the other three from the corresponding elemental dailies – the Pandaren Spirit Pet Supplies.
Video links are from my Elekk and levelling teams on YouTube.
On a side note, Mumper confirmed the drop rates on rare stones are low from battles. “Pet daily quests offer a better rate but still not easy.”