Xbox – do local split screen without a network connection in Halo: Reach

To add a bit about what tzenes said: It is confirmed that Bungie plans to release the campaign matchmaking some time in the future:

"If you're looking for campaign matchmaking in Halo: Reach, sit tight. In an effort to keep your first campaign experience spoiler free, we've decided to wait for a bit before we deploy the campaign playlist.

From here: http://www.bungie.net/News/content.aspx?type=news&cid=28616

How does it work? How am I matched with other players?

Here is Microsoft's article for the match making system of XBox Live (So contrary to other answers, yes, there is an answer to this, but you wont get the math specifics)

http://research.microsoft.com/en-us/news/features/trueskill.aspx

Is there a difference between the cooperative modes (ie firefight) and the competitive modes (ie slayer)?

While I play the game, I can not be sure.. This would depend if they set up the play modes as separate comparisons within the TrueSkill system. I would say this was Not done however, and a players skill is regardless of game type.

How can I improve who I'm matched against/with?

I am not sure entirely what you mean by Improve, but in general just playing more games will settle your TrueSkill score pairing you up with people who are equally skilled as you. As the article reads, it does not try to pick dead match team games, but will try to pair dead matched players and put them into opposite teams.

FYI, This is the match making of all XBox Live games since Halo 2, as according to the article. From RobV in the comments though, the insignia represents how much/how long you have played the game as opposed to a graphical representation of your match making ranking.