Now, it's no secret, I hate pbp. It's super slow, most of the effort goes into character creation and backstory, my least favorite aspects of the game, and it perversely relies more heavily on team participation and provides less of a group experience than traditional RP. In my experience, naturally.
That said, I've found some solid use for it in my game. It is a boon for solo roleplay, it can lead to some non-traditional experiences, flesh out experiences that were moved through more quickly in the regular session, and such.
To that end, I'm posing tips and concepts that can improve one's pbp value per post. It shouldn't be seen as simply useful for pbp though, because the ideas can be extrapolated to work for any collaborative effort, including regular role play.
Offer information and direction. Don't say "What do I see?" or even "What buildings are there?" This is horrifically generic. Be specific, but make certain you are not excluding options. For instance, if you are looking for a weapon, don't necessarily ask "Is there a sword shop here in town?" "Is there a place where I can buy a sword?" leaves open other possible options. But don't ask what you see, and then take three more exchanges before you point out you were hoping to buy a sword.
Do it IC rather than OOC. To use the above example, improve the question even further by doing it in character. "Einar asks around for directions to a place where he can buy a fine sword." This has the advantage of now putting action into the game. An interaction between character and NPC is superior to one between DM and player.
Do more than less. Asking one question at a time drags out a non-real time exchange. Consider the following:
Lavinia: Lavinia looks around for Katrina.
DM: You find her.
DM: She's at a restaurant
Lavinia: Which one?
Lavinia: Ok. IC: "Hi, Kat."
Lavinia: "How was your day?"
Kat: "It was nice"
Lavinia: "I'm pregnant"
Katrina: "Heinrick's going to be happy."
Lavinia: "It's not his."
Katrina: "Uh oh."
Holy ****. Seven posts to say hi. Ten to get through pleasantries. That might be ok in real time, but that's probably over a week in pbp.
Lavinia: Lavinia looks around for Katrina. Once she finds her, she exchanges pleasantries with the archmage before coming to the crux of her concerns. She's pregnant with twins, and only one of them has any elven blood.
DM: You find Katrina at Maurice's, paging through a menu loaded with seafood dishes while the buzz of customers hums in the background. The massive human waiter stands off to the side of the table, awaiting your pleasure, as the savory scent of high priced food wafts in from the kitchen. The smooth polished table gleams slightly as the sun reflects off of it through the new skylight, an architectural addition since the blast that destroyed the old building.
Katrina: Katrina speaks an arcane phrase and flexes her supple fingers into a spell to divine that the pure human child is Einar Sigurdsson's. She darkly suggests Lavinia try to pass it off as Heinrick's own, since half elven blood sometimes skips into future generations before moving on to more important topics. She asks Lavinia what developments have been made with securing the land rights for the shipyard currently under construction.
The latter exchange is superior, because not only does it more expediently cover the conversation, but each person is taking and giving. Lavinia sets up the scene by getting right to the non-assumed bits. If she wasn't going to find Katrina, the DM should have said "No" when one of the two asked if they could pbp a conversation between them. And it should be assumed she's going to say hi, and probably open the doors before walking through them, and most likely has put on clothes before venturing out into the streets. The pregnancy is something that Kat and the rest of the actors don't know about yet, so she advances the narrative right to that point. She can't assume how they will react, so that's the end point.
The DM in the first exchange was sucking too. The questions were vague and annoying, but one word responses is a bad way to build up your world and invest players in it. The latter scene really gives some flavor to this Maurice's place, and maybe some things to follow up on. A massive waiter? Why are they so big at Maurice's? A blast that destroyed the restaurant? That's a connection to the past for old players and a tidbit to follow up on for new ones. And then the loading of sensory information.
And Katrina provides both a response to Lavinia's hook and then gives a hook of her own. Lavinia's player now has something to respond to as well, rather than in the first exchange where Kat was just taking in the pregnancy news and not shelling out anything. Once the pregger's convo comes to a close, the shipbuilding convo can pick up.
Use sensory images. This is just a general DM tip, but it works for players too. You insert two to three senses in every post, you'll be providing a richer experience. If you work four-five in there, you are hitting the jackpot. Trying to figure out what you smell or taste or feel forces you to think about the entire scene, and when you are thinking about the entire scene, it becomes bigger by default.
Include action with your dialogue. Speaking is good. Speaking while describing your gestures, whether background, incidental, or vitally pertinent to the language makes for a richer experience. This is whether or not you are posting actual dialogue or synopsis conversations.
Good cooperative efforts require both actors to be reading each other and pulling back and forth as best suits the scene. It is a delicate play between stepping back to let the other person shine, stepping forward to help them into a better position from which to shine, and also not missing your own moment.