All the World's a Stage
No one can tell you exactly how to roleplay anything, so take below as a helping hand and a guide - not a rulebook.
This guide will help you understand a Pandaren.
Where you come from Edit
You came from the Wandering Isle and as the name suggests, this island wanders (due to the fact it's a giant turtle.) One way to add this into roleplaying can be when Liu Lang started recruiting followers to join him on his quest to explore the world, you could say your ancestors joined him on his journey.
Or your character could be from Pandaria, not having known anything about the outside world before the mists parted, then you would of course have to choose as specific town/city/village in Pandaria, but.. meh, it's opening up for much more RP, you can be a part of the Shado-Pan, you can do many other things..
Culture and History Edit
Pandaren are quite honorable; they live every day like it was their last. Back when the ancient Mogu had ruled Pandaria, they were fierce dictators. The colossal statues that dot Pandaria were built with many resources and many Pandaren slaves. The Mogu did not let the Pandaren use weapons, only their paws, feet and tools you would find in a farming shack, like a Quarterstaff. Eventually when the Mogu Empire started to weaken, the Pandaren staged a revolt, thus succeeding in overthrowing the Mogu Empire.
Before the night elves became addicted to magic and lured the Burning Legion to Azeroth, the Pandaren were very close allies with them. Some of them even lived with the night elves and witnessed the power of the Well of Eternity. Yet after the night elves became obsessed with the well, the pandarens decided to sever the tie and enclose their border in Pandaria.
During the bleak days that preceded the sundering of the world, when demons flooded onto Azeroth and threw the entirety of the mortal realm into jeopardy, the last Emperor of the pandaren discovered a way to protect his land from the devastation. His deal with fate shrouded his land within an impenetrable mist for ten thousand years, but the nature of his transaction has left Pandaria haunted ever since. Previously, ships entering the mists have lost their bearings and spun about aimlessly before returning to the open ocean. As for the pandaren, they looked out toward the mist-veiled seas and many presumed that the rest of the world had perished in the Sundering.
Many generations ago, a particularly bold pandaren named Liu Lang set out to see what was beyond the mists by setting sail upon the back of a giant sea turtle: Shen-zin Su. As the turtle grew, so did Liu Lang’s desire to explore the world. Others joined him, until eventually a whole colony of pandaren explorers travelled the ocean, living atop the expansive "Wandering Isle". Although the Wandering Isle hasn’t made landfall in many years, those who live there are still ignited by the spirit of adventure. Chen Stormstout is a native of the Wandering Isle, as are any players who choose to create pandaren characters. They are a rare breed, on the whole far more adventurous than their land-locked and long-lost relatives on mainland Pandaria. When the great turtle is threatened, and their whole wandering homeland is in jeopardy of being swallowed by the sea, players will have to accelerate their training and spring into action. Sometime in the wake of the Cataclysm, the mists abruptly vanished. Alliance and Horde naval fleets, engaged in skirmishes around the world thanks to the new Warchief’s aggression, suddenly found a new continent where once charts showed open seas. With both factions escalating their feud into a global conflict, the war for Azeroth shifts in a new direction.
Ever since the pandaren empire dissolved, pandaren society has been divided into shao'dins. A shao'din is the pandaren name for one of their clans.Each pandaren belongs to a shao'din, which is usually led by a shodo-pan. A shao'din usually has a military wing comprised of wardancers who report to the shodo-pan.
Due to the nature of their sheltered past and people, it is likely more forgivable than other races for a Pandaren (and thus the person who Role-Plays one) to know little or nothing about the major events (and lore) of the rest of Azeroth, asking and learning about such things from those he or she meets.
Pandaren are the only race that are neutral, meaning that they can pick their faction.
Picking the Tushui means living a venerable life through meditation, rigorous training, and moral conviction. Aysa Cloudsinger is one of the pandaren that have mastered this art. Your character's personality should be around this, and probably should have a calm demeanor and a relaxed way of handling things.
Picking the Huojin means stating that inaction is the greatest injustice, and that there is no shame in defending one's homes and loved ones regardless of cost. Ji Firepaw is a staunch follower of this way, and the first of them who recognized the similiarities of this way in the races of the Horde, and all that find themselves closer to this belief have decided to follow Ji and stand united with all these Horde races, whose desire is to live free. Your character should have a brave and daring personality, and should be able to act at moments notice.
Keep in mind that the tushui and huojin are orders of monks. Not every pandaren needs to roleplay as a member of them. Many pandaren simply wish to explore the outside world, and could act as mercenaries, adventurers, or explorers.
Monk: You are a Monk. You follow age old tradition of fighting with your fists, hands, and a few weapons. You would be highly respected in your society, seeing how you are practicing the arts that had freed your kind. Many will look upon you with curiosity, seeing how your new allies have never seen such ways to fight. Or maybe they have in the form of Scarlet Monks.
Warrior: Warriors are a very interesting class to be as a Pandaren. The Mogu had outlawed weapons, after all. After the Mogu's downfall, your family could have possibly started learning the art of weaponry, and started passing it down to younger generations in your family. On the other hand, you could be someone completely new to the art of weaponry, first learning on the Wandering Isle, and learning even more by your new allies, who have had much experience in war. Also keep in mind that the pandaren have a long history of weapon-based combat and tactics. Many warriors may wish to roleplay wardancers: the pandaren version of knights, the Pandaren version of regular warriors being pikemen. They are typically very well respected in society and command respect from their peers.
Mage: Mages are very interesting to play as a Pandaren. Before the Night Elves became addicted to magic, your family could have possibly learned the Arcane Arts from the Night Elves, and started teaching it to your kind. Or they could have learned magic from the Jinyu, who are able to speak and tell the future in the water through magic. Pandaren mages could be seen as esoterics, scholars, and intellectuals that learn the magical arts.
Hunter: Every race have hunted in their own way. The Pandaren on Pandaria had to hunt for food, right? Many exotic animals roam the jungles and mountains of Pandaria, ranging from Quilen, Cloud serpents, Dragon turtles and much more. After leaving the Wandering Isle, you could be curious for all the different types of beasts in all of Azeroth. In times of war, pandaren also employ archers and other marksmen in their ranks, along with their pikemen and wardancers.
Priest: The light is a difficult subject for the Pandaren... They have never experienced the light. The only way you could have learned the powers of the Light were after you left the Wandering Isle but it is also possible the Light is seen as type of magic, like the arcane or fel, not as something worshipped. It is also possible that the pandaren spiritual outlook allows them to harness the same energies that humans and draenei know as the light, despite having a seperate (albeit similar) philosophy. Many humans see the light as an energy formed by positive emotions, so this may be the case. Pandaren priests could be seen as esoterics, scholars, or philosophers that study the ancient traditions and belief-systems of their people.
Rogue: No, Pandaren do not have those Shady types in their society, instead, Scouts, Spies and Assassin's are use by the Shado-Pan, in the form of the Wu Kao..
Shaman: Pandaren Shaman are quite notable, especially for brewing ancient remedies for diseases and sicknesses. Pandaren Shaman follow the disciplines that are very close to Daoism (Treating the world with respect.) When the demons came to Azeroth, a enormous shroud of mist surrounded Pandaria. The Pandaren thought the world had ended, and had decided to learn to preserve the rest of the land that remained.