I'd say format it as dialogue, with each person speaking on a new line. When it comes to the actual text, keep enough chatspeak to make it realistic but please don't put too much in. Too much chatspeak would be hard to read and some might not put in the effort.

I'll write this as a list (I like lists).

- Formatting I'm perpetually perplexed by how to format chat room "dialogue". Probably due to the newness of the media form, there's no real convention on how to do it. Generally, in books I read, it's in a different font (sometimes different for each character), with the screen name, a : symbol, and their message, each on a different line. I don't know if you can submit manuscripts with different fonts, though, so usually when I write chat rooms, I just italicise. The other problem is how to separate chat dialogue from the rest of the text, eg.
------------
Fred logged into the chat room.
Tom: Hello?
Fred: Hi!
-----------
Do you put a double line break:

between the paragraphs and the chat? or just a single indented line. It looks weird if someone goes on and on like this and it's indented though:

Fred: I'm going on and on and on and on and on and on and blah blah blah to demonstrate Kibble's point about how chat room texts look weird in normal paragraph form where the text comes back closer to the margin than the indent on account of that's not how it would look in a real chat room (everything would be indented from the name down).

- What to include I personally think it's realistic to include some automated messages, eg. "Tom has logged into this chat room." But in a long conversation, timestamping each message to the second might be a little annoying for the reader.

- What they say Generally, people I know don't discuss much of importance on chat rooms. Mostly what they've been doing, people they know, and news. This would be different, though, if the chat room was the only available form of communication.

- How they say it txt tlk doesn't seem as popular in chat rooms, probably because you don't pay by the character. txt tlk is hard to write and read, so most people use it for texting only, to save money. However, some things, eg. 2=to, too; less commonly 4=for are used, as well as r (are) and u (you). Those are the main ones I see. Also, remember to be inconsistent; a character might use "2" in one message and "to" in the next.

The first letter of sentences is often uncapitalised, however, and sometimes names are (depending on whether the writer feels it is disrespectful to write someone's name without capitals). Sometimes people remember full stops (periods) and sometimes not; commas are also rare.

One thing that happens on chat rooms is people may post more than one message in succession, not because they thought of it later, but as a sentence/paragraph pause (multi sentence messages are rare; multiple paragraphs in one message are not possible on many messaging programs). So you'd use it for a dramatic pause, etc. eg.

Tom: guess what
Fred: what?
Tom: yesterday I was walking 2 school
Tom: and i saw Bob
Tom: and he was shoplifting

You are not paying for each letter, but you may be paid for each.

I would use proper speech and simply format it correctly unless you are doing a cyberpunk world in which slang and fragmented words will appear in the behavior habits of such a culture.

What you'd need to remember to do in a chat room is that everyone types a little differently.

So, for instance, you could have one chatter who would be grammatically correct, and another who abbreviates every other word. You'd then need to keep that up, because it would be a little odd if someone immediately transcended from 'spkn lyk dis' to using complete words and sentences!

Also, you'd want to make sure the conversations weren't boring. A lot of times in chat rooms, the conversation will be stuck on pretty tedious subjects. However, you'll also want to make sure that the conversation bears a semblance to reality. Just get the fine balance.

Lastly, some things in the chat room could possibly be italicised or bolded. For instance, an automated message could be in bold or something. But you can work all of that out.

Hope this helps!

~Amy