Lets dive right into it. The format itself. It doesn't really matter what game system the GM is using, whether its Dungeons and Dragons, GURPS, Shadowrun, or a more free style game. The entire crux of the game is based on posting to the game forum. Because of this, games can take a long time to work out as players and GMs go through the process of reading all the current posts and working up a reply to them. Most of the work is heaped on the GM, since its his or her game after all. Yet the players determine the overall speed of the game. Generally the GM is ready to keep the game moving along, checking in on the progress daily (or as real life allows). That is the other beauty of the game, you can read and post as your RL (real life) allows, everyone from all over the globe can play the same game each on their own schedule.
Most games are turned based, the GM will post the setting, and any relevent information about NPCs and the like. Its up to the players to have their characters respond to this setting. In general every player should reply to every post the GM makes. While you might not always feel that your character has much to do, or much to say in the situation at hand, the GM won't know this. In my own games, I like to wait for each player to have a chance to respond, for each character to interact with the world around them, even if that means they sit tight and listen and watch what is going on. Even that type of post lets the GM know what your character is doing and that he can move the game forward. This is doubly important if combat or another such cirtical moment is at hand. (ie A ship just struck a reef at sea and characters are pitched overboard.)
So the best way to keep a game moving along smoothly and 'quickly' is to make timely replys to all of the GMs posts. Also this could mean responding to other characters in both conversation and in actions. Many GMs will not have a problem with characters conversing back and forth for a few postings inbetween the general GM posts. As for situations where you don't think you character would interact, keep in mind that unlike pen and paper games, the longer characters simply 'sit around' the longer it takes for anything to happen. In most PbP games, characters are ment to be heros and as heros they generally have to interact for anything to happen. "Fate favors the bold" they say in Rokugan (Perhaps my 3rd game setting).
Lets talk about posts themselves. Posts should be as colorful and as descriptive as can be. Since you aren't sitting around a table with your friends, you can't pantomime to the GM your actions of swinging your sword, nor can a GM in a PbP game see the scowl you are making for your character's face. One and two line posts, show little interest in your characters and in the hard work that the GM has put into the game. Every character, even if sitting on their butts doing nothing, can be described in detail. Is that character holding any of his weapons or gear, is he watching intently, or stareing off into space? Does the wind tug on her cloak or does the sun glint on her helmet and spear? These general enviornmental details for a character can add much wanted life to a character, even if they are passive.
Its become a convention on this website to use Italic text to show a character's internal dialog. While this information can't really be used by other characters, it great to read for flavor and character delevopment by both the GM and the players. While not always suited to the situation, its a nice touch at times.