This tab in the lobby is how you start to play Forged Alliance with the client. As long as you have Supreme Commander Forged Alliance installed, no further setup is needed.
Remember, you need to start the game through this client for all the improvements to work.
The Matchmaker is the Over arching replacement of the Ladder secion as it now encompases the 1v1 & 2v2 matchmaking, and also has plans for a 3v3 & 4v4. For Mor information about the Matchmaker See the Team Matchmaker page.
This is how most games are played - simply double click on a game which you like the look of and you will join it! However, bear in mind the game titles - some have rating requirements, and you may have trouble vs players who are much higher rated than you.
To learn more about the Co-Op Campaign and the all the Community made Custom Mission please go to the Coop Missions page.
In addition to the AI that are available in FAF by default, there are a number of advanced custom AI which can provide various gameplay experiences and offer a significant increase in challenge over the default AI - this article provides further detail of the custom AI available on FAF and how to play using them.
You can have any combination of human and AI players, as you wish.
You can host a game by double clicking the icons on the left of the window to open a game dialogue with a variety of options.