FAF (Forged Alliance Forever) is a non-profit organization whose overall aim is to support the open and continued development of the game Supreme Commander: Forged Alliance (SCFA). When people say FAF, they may mean the FAF client, the FAF-maintained version of the game itself, the FAF Association, or the community of FAF players.
Steam link/GOG link can be thought of as a one-time verification tool that allows us to make sure you own a legal copy of the game Supreme Commander: Forged Alliance. Verification using either the Steam link or GOG link is required to demonstrate proof of ownership (for legal reasons, as well as to reduce smurfing). However, if you own a retail version of the game, but don't have it on Steam or GOG, you should be able to use your CD key to redeem a licence on Steam for free. Alternatively, if you don't own the game or need a new copy, you can purchase it via Steam or GOG to play on FAF. If you own the GOG version of the game, you can follow these linked instructions. Alternatively, once you have the game (Supreme Commander: Forged Alliance) in your Steam library, you can link your account to Steam (your Steam profile and games list will temporarily need to be set to public for this to work, but you can hide them again afterwards). If you have concerns about this process, you can read the technical explanation of why it's safe, and you can also note that FAF has an active community that can answer questions, FAF has existed for over a decade, FAF has had hundreds of thousands of users, and the FAF Association is a non-profit organization. If you need more help setting up the Steam link, click here.
You can join the FAF Discord and talk with people there (you can also message people via the FAF forums and via the FAF client). A lot of people check the FAF Discord frequently. So, if you join one of the general voice channels on there, you'll likely get some company in not too long. You can also ask people in-game or in-lobby with you if they want to talk on Discord. People often say yes.
You can check out the help section of the forums, or ask for help on the FAF Discord in either the tech-support-foruml (for technical problems) or in the #training channel (for gameplay questions, finding trainers, and improving at FAF).
FAF provides integrated mod support, better AIs, multiplayer campaign missions, community services, a matchmaking service, easy access to thousands of new maps, the ability to have games with up to 16 players, a random map generator, a lot of lag reduction, bugfixes, QoL improvements, and improved game balance. To learn more, you can read this more detailed explanation.
You can join the 'All Welcome' games, host a game yourself, or play on the matchmaker. Playing rated games and winning some will help you build your rating, and getting a higher rating will enable you to join even more games.
You can check out this link to see the things that can make games unrated. If there is nothing that makes a game unrated, it is rated.
If you haven't already done so, you can download and install the FAF client, make an account, and log into your account on the FAF client. There is a Maps tab and a Mods tab near the top of the FAF client. You can browse, search for, and download maps and mods on those tabs.