Now there are many different methods of rp, so one cannot say that you have to use a certain method.
It should be noted that there are some things you really do have to do. These things have nothing to do with method or type of rp.
And I say these things because they are problems which I often encounter in attempting to rp with people. So here goes:
1) Interact with the first post of the rp. Seriously. The first person to post is setting up the rest of the rp. Just leaving them hanging and doing your own thing does not progress the rp or spur character development. DO NOT LEAVE the first person to try and figure out how to get all of the characters interacting. They did setup. You should be doing follow-up. If you want to write individual character novels, do that instead of rping.
2) Don't skim posts. It's a bad idea. It causes you to miss important things that someone posted, so you wind up ignoring those important details, and then the other person has to basically throw away what they had written. Once again, this is basically rendering the other person's post as pointless, and is not good practice for rping with other people. It's like a social courtesy, almost.
3) Be mindful of stage set-up. Even if you are not the sort of person who does this, odds are that you will encounter somebody who does. If their character is in a particular place or position in correspondence with something or someone, try to be aware of that position which the player has described. If they said that they were behind you, with their back turned to you, don't just say "my character looked up into your character's eyes". Seriously. Describe the act of your character turning around and maneuvering around the other character to face them. It's not that hard. You don't have to be really good at writing in order to do this. You can use all the typos, bad grammar, and basic words you like. Just work with the other players on stuff.
4) Keep the role consistent. It's rp. Role play. You are playing a role. Act the character as the character would act, not how you or somebody else would act, or how you think the other players want your character to act, or how you think they should act because you, personally, feel sorry for the other character. Seriously, for the love of waffles, DO NOT DO THIS. You will a) throw off the whole rp b) probably screw up the other character more, because the other person is sticking with their character's personality, c) it's just dumb. Play your character how they are. Don't try to force things. The other players want the rp to flow naturally, anyway, they don't want you to do anything in particular, just rp naturally. It'll all work out, don't worry. IT IS JUST A GAME.
5) Don't overpower your character. Give them some weaknesses, for waffle's sake. Any kind of weaknesses. They could despise pears, or they could be sickly, or a coward, or maybe they just have a bad personality. But also, don't give them so many weaknesses that they're annoying to rp with. I mean... keep it kind of realistic. Not that all rps are realistic. But every universe or story has a logic of its own, so try to stick to that. What I mean is, make your character a person. Make them believable. Tangible. Balance them out a little. Don't make them perfect, because nobody is perfect. Don't make them devoid of any redeeming qualities or skills, because frankly no one is like that, either. And no one likes a whiner. If your goal is to make people feel sorry for your character, they probably won't. And will just hate them. And not want to rp with them.
6) As ~Rhapsody-Shaman
pointed out to me in comments, if everyone else that you are rping with in a group setting is rping in paragraph format, describing their character's actions and all that jazz, PUT IN THE EFFORT to do at least a few sentences. Describe your character's actions, too. Don't be that guy who walks in like a noob after these clearly well thought out posts and types just what your character says. If you don't want to rp more than that, then rp with only other people who will merely talk for their character. It's not that it's a worse way to rp... but it's really annoying to do that in a setting where everyone else is actually putting thought and effort in.
7) Don't get mad at people who are writing in a more serious tone than you are. Some people prefer to focus on character development and such, and that's up to them how they go about it. If you have a problem with it, don't rp with people who are serious.
8) Don't get mad at people who are writing in a more silly tone than you are. Some people prefer to just let loose and be crazy, and that's up to them how they go about it. If you have a problem with it, don't rp with people who are silly.
9) That being said, most silly rp is considered "crack rp", and is not in most cases considered canon. Try to avoid excessive nonsense in normal rps, because it can be annoying to the people who are actually into the rp and want to play their character, rather than just playing around with their character. Again, nothing wrong with crack rp, but try to contain it to crack rp. You can use humour in normal rp without just going completely mental. (Especially if you're being mental just because you are uncomfortable with serious rp. That makes you that awkward dude in the theatre who cracks awkward jokes loudly just because he's so obviously insecure. You know what I mean.)
10) Don't make characters based on existing characters by someone else. Really. Just don't. I pretty much guarantee that you'll wind up just looking like a noob with that one. The template will be obvious to anyone with experience, and it isn't good practice for you, and it will not be good for your reputation as a role player, so just don't go there. Using creativity in making a character is going to make you better at rping them. Seriously. What's the biggest problem with a Mary Sue character? They're so clearly a shallow combination of traits that the writer has liked about other characters. Don't go there.
11) I'm sure there're plenty more, but I've lost my train of thought. So if anyone else has some suggestions, I'll gladly add them to the list.
So now you all should know how to rp. Good luck out there.