This will add another field to the form so you can enter the site's address domain name (URL) of your site. You can then login with your username and password, the ones you use to log when using a computer browser.
If you are already logged into a site in the app and you want to add another self hosted site, go to My Sites and click on the + button, then select the link to 'Add self-hosted site.' For this option, enter the username, password, and URL associated with that site.
Here's a Video: https://youtu.be/FwsV5PyWOAo
You should see the log in screen with a blue "Log In" button. Tap that.
On the next screen, you'll see a space to enter your an email address. You'll want to enter the email address associated with your WordPress.com account, then tap "Next" (note: since this is a WordPress.com site it's important to use your WordPress.com credentials and not your site address)
On the next screen you'll have an option to be sent a magic link. Some folks run into trouble here, so instead tap "Enter your password instead", and enter your WordPress.com password into the field, and tap "Next"
(Optional) if you have Two Factor Authentication enabled on the account, the system will have already sent a verification mode to your authenticator or mobile number. You'll need to enter it on this screen. If you do not have access to your 2FA device, let us know.
Once you tap next you'll see a screen that shows you your username and some of your sites. Once you tap "Continue" you're successfully logged in!
Here's a Video: https://youtu.be/GEq2lf_q1SY