• In the upper-right corner of any GitHub page, click your profile photo, then click "Settings" ("gear" icon).

• In the "Access" section of the sidebar, click "Password and authentication".

• In the "Two-factor authentication" section of the page, under "two-factor authentication":
• Under "Authenticator app", click on "Manage Authenticator app" (... icon), click on "Disable". The page will refresh.

• Under "Authenticator app", click "Add". This will display the QR code image on the page.
• Open in the smartphone the Authenticator app. Click on the + icon to add an account.

• Click on "Other". Scan with the phone camera the QR code on the GitHub web page above.

• After scanning, the Authenticator app displays a six-digit code that you can enter on GitHub.
• The Authenticator app saves your account on GitHub.com and generates a new authentication code every few seconds. On GitHub, type the code into the field under "Verify the code from the app". Click "Save".

References:

Configuring two-factor authentication - GitHub Docs - how to set up two-factor authentication from scratch (before Authenticator was used for the first time).

Just configured 2FA on two separate computers, both using the same type of method (browser authenticator app -- https://authenticator.cc/). The process is as follows:

• Login using your current method.
• Under https://github.com/settings/security, click on Edit for your preferred method.
• This will generate a secret key, treat it like a password, and save it securely.
• Use this key to setup the authenticator on both devices.
• Click on the authenticator app icon, then the pencil icon, then the + sign, select Manual Entry, set GitHub as the issuer, then your secret key, and your username under the Advanced tab (I didn't change any other setting there).

You should be able to login without problems on both devices using the same type of 2FA method.

I cannot comment on other methods, but this worked for me and maybe it will help someone.

If you haven't already, download a TOTP authenticator app on your mobile device.

Popular options include Google Authenticator, Authy, and Microsoft Authenticator. These apps generate time-based codes used to complete the 2FA process.

Then proceed with the following tasks sequentially:

1. On the Settings page, find the "Security" tab on the sidebar.

2. Under "Two-Factor Authentication", click on "Set up two-factor authentication". You'll be presented with options like 'Text message' or 'Authenticator app'.

3. Since you have Google Authenticator, choose the 'Authenticator app' option. GitHub will display a QR code on your computer screen.

4. Use Google Authenticator to scan this code. This links your GitHub account to the app. After scanning the QR code, Google Authenticator will provide a 6-digit code.

5. Enter this code on GitHub's website where prompted