Case 1: You forgot your password
Use the reset password form on the website
Case 2: You forgot your password and don't remember your username
Did you really forget it or did you just forget that you renamed your account recently? Ok let's assume you forgot it:
Solution A: If you know your accounts email address, you can login to the website using your email address. Click on the user symbol in the top right, there you can then see your username.
Solution B: Use password reset via Steam. After the Steam login you are redirect to a page that greets you with your username.
Case 3: You forgot your password and the email address of the FAF account no longer exists or is inaccessible
Use password reset via Steam. After the Steam login you are redirect to a page that greets you with your username. After the login change your email address!
Case 4: You forgot your password and the email address of the FAF account no longer exists or is inaccessible and you have no access to your Steam account
Unless there is a moderator who knows you personally for years and can vouch for you, you are screwed. Since we can't verify your identity all you can do is create a new FAF account, buy the game on Steam once again with a new Steam account and link the new FAF account with the new Steam account.
Case 5: You forgot your password and the email address of the FAF account no longer exists or is inaccessible and the account was never linked to Steam
Unless there is a moderator who knows you personally for years and can vouch for you, you are screwed. Since we can't verify your identity all you can do is create a new FAF account, buy the game on Steam and link the new FAF account with Steam.