Conversations are not the hardest things to write… But there are a few differences from others. So with that in mind here are a few tips.
When you're writing conversation stick to first person, present tense for all conversations. Even if you're writing the story from third person past tense. The reason for this switch is that for your character the world is still happening to them. Things are occurring in the present for them and all conversation is from their perspective. (The third person, past tense is used for describing their actions… Even if one of their actions is speaking. Any speech is still told in present tense.)
Read all posts carefully looking at dialogue of their character. Spoken word is actually only one aspect your character can pick up on. (Just like in real life, a lot of communication we make each day is never spoken. We tell by looking at others and determining based on that solely.) Body language can help tell you more about the situation. Whether it's the way their character is standing/posed or a face they make.
Consider:
"Where are you going?" He asked. "I'm going to the mall" she replied.
Versus:
"Where are you going?" He asked. Upon hearing his question she rolled her eyes. Finally, she replied: "I'm going to the mall"
The latter has a facial motion in there that can tell that she didn't like the previous question. This provides more context for a situation and gives you more to work with.
Though you don't always have to reply to each and every facial expression or body stance/pose. Take into account what your character would notice. Are they doing something while speaking so that their focus isn't on the other person? (Thus less likely to actually see their expression.) Or are they not particularly great at picking up on facial expressions or body language? (Some people struggle with this a lot.)
When you're reading and beginning to write a reply, be careful what your character knows and what you know. You (the player) may have access to information your character doesn't (like if the other player includes things like their character's thoughts). So be sure to read through their post (or posts) and distinguish that so when you're replying later you don't accidentally include things that your character wouldn't know.
(Though this may not always hold true. For example, if a character is psychic and can read minds then they may know what your character has just thought and can reply to it. But for most part characters can't read each other's minds.)
Like in the previous section, use your character's body language to help bolster what your character actually states. This allows for other players more to play with.
Feel free to comment on the surroundings/situation. Many times you can use the surrounding environment to have a character make comments on. Things like:
Also never be afraid to have your character try to change subjects. This can give more for a player to respond to if they want. They can have their character:
Though when using those tactics, keep in mind your character's personality. Not everyone likes to talk that much and/or they may not respond the same way so for example they might not make a comment on what other people are doing because they don't care what others are doing.
Rude characters can be harder to write conversations with because they tend to give short, blunt or cold replies that are innately designed to shut down conversations. So for them be sure to use facial expressions and body language to help supplement what their character states.
Converse to previous section, you also want to watch how much conversation you actually have. Too much conversation (especially if there is also a lot of action going on) can make things more difficult for others to reply because:
(Splicing dialogue in isn't necessarily bad, it just makes things slightly harder to read and follow along.)
For a good balance… 1-2 sections of speech is probably adequate. 3 might be pushing it a bit. Though this depends a lot on length of speech, context and situation. Like if your character is delivering a lecture, then no one should be interrupting them. But if they're talking informally to a friend they probably wouldn't be delivering a 6 paragraph speech. (Though this isn't a hard and fast rule because there could be situations where a character is ranting and says a lot.)