The login process for the browser extension is almost identical to that of the mobile app. Remember, you need to have a Burner account set up through the app before you can use the extension. In order to log in, simply type in the same phone number you used to set up your Burner account (you can not log in with a burner number).
You will then receive a text message on your phone with a 6-digit verification code. Type in the verification code, and you will be able to use the extension. Simple as that!
If you want to log out of the extension, just delete it. To log in with a new account, just type in your new phone number when logging in and follow the verification steps listed above.