Alright, so firstly, I should discuss what RPing (role playing) is, by definition.
Role Playing (RP) is a form of storytelling where the Role Player is one of the characters in the story. The GM (game master),creates a story arc, and we the role players make choices that change what occurs.
Some choices are insignificant, like greeting the gardener (though the GM may use that as a future plot point. For example, the gardener happens to be your foe, and your act of kindness stopped him from fighting you. But for right now, we will assume it is insignificant). However, some choices will change the story completely. Deciding factions, going to Death Valley instead of Happy Trails, bullying the king, etc. These choices will change the game's path, and it is crucial that we think out our decisions before acting upon them.
Not to say that you shouldn't think before every post. You MUST think before you post, since it gets irritating if one player doesn't think before acting (unless their character is a complete moron. -I'll get to this later)
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Stats:
This is a short section, but rather important.
When you decide on a stat level, you are setting your characters stats. If you are playing as a character with a '1' intelligence (INT), you can't quote Shakespeare, and if you are playing as a genius, you can't speak like a moron. (AKA "Me Are Tolkien, Me love Books" is not acceptable/logical :P)
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Staying in character:
A sub category of "Stats", but equally important. Your character must stay in character at all times.
If you describe your character as a kind person, you can't make him vicious, and if you describe your character as a womanizer, you won't be supporting women's rights. etc
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How To RP:
The most important section, and the one I don't describe. :P
The basics of RPing can be learnt on these threads:
http://chooseyourstory.com/forums/forum-games/message/8040
http://chooseyourstory.com/forums/forum-games/message/8631
The main difference between our RPing and the ones described above is that their posts describe Free Form RP while ours is a mix of pbp and free form.
pbp's require the GM's hand in nearly everything during combat situations. Walking down a road is guaranteed, but you may encounter goblins whilst you walk. The GM decides these things through dice rolls and/or common sense.
However, when you aren't in combat, normal acts will not require rolls. Thus, you can say that you walk across town, arrive at the super market, and order a pizza, without the GM rolling anything (aside for Charisma for Pizza price).
Basically, unless doing mundane stuff, don't assume you succeed in anything. You can assume you run towards the Goblin, and that you slash, but you cant assume you killed it.
(NOTE: While some tend to go for flowery posts during combat, I find it ridiculous so I post short during combat and longer for non combat. But do whatever you find comfortable)