Where the service offers it, the sign-in and sign-up pages show Continue with Google or Continue with Microsoft. You are taken to the provider, sign in there, and come back signed in. If your account here uses two-factor authentication, the code is still asked for.
An account you already have. If the provider confirms the same e-mail address that you confirmed here, the two are connected the first time you use the button. Otherwise sign in with your password and connect them under Settings → Security → Sign-in methods. That extra step keeps out somebody who merely typed your address into an account elsewhere.
An account made with Google or Microsoft has no password at first. In the browser that is all you need. The desktop and mobile apps sign in with e-mail and password, so set a password under Settings → Security before you use them; a link is sent to your address.
Removing. Sign-in methods lists the connected accounts, and Remove disconnects one. The last way to sign in cannot be removed: set a password or connect another account first.
The provider tells the service your name, your e-mail address and the identifier of your account there. Nothing else is asked for, and the password you use there is never seen here.