The MP side of the game can be thought of in two ways - a chance for you to play with mates, and a chance for you to spend a lot of time waiting for a pick-up match.... The former is obviously potentially a lot more fun than the latter. Just saying...
When you start an MP game you have the following options:
The selections above are pretty self-explanatory. For a VS match you are competing against the other player, and for a COOP match you are playing with them.
For the Quick Match options the server will attempt to match you with another player who is also seeking to play but be warned, while this is relatively easy to do on weekends, getting a match any other day of the week is often a matter of luck.
Playing with mates on the other hand is a given and, naturally, tends to be a bit more fun as well.
As awkward as this is to say, for the vast majority of players the multi-player side of the game is really going to end up being little more than what effort is required to unlock the Achievements that are part of that. Sadly with the exception of specific types of games (shooters for example) multi-player these days is not as popular as it once was!
That said, the following Achievements represent the MP side of T5:
Good Sportsmanship (10G) Finish a multiplayer game.
Project Beale (20G) Win a multilayer game by points.
It Prints Money! (20G) Win a multiplayer game by money.
Architerissimo (20G) Win a multiplayer game by construction.
Naughty Docks (20G) Connect a dock with that of another player.
What Energy Crisis? (30G) Produce and share 1,000 MW of Power with another player.
That is pretty much the whole run as far as the MP Achievements are concerned. Sadly you are not going to manage them in just one or two games - for even with the willing participation of a boosting partner you are still looking at four games minimum.... Each.