How can I recover my email passwords?

The method used for resetting your email password will vary depending on your email provider.

Here is an article from Apple that will help your reset your Apple ID / iCloud password.

https://support.apple.com/en-us/HT201487

But for other email providers (Google, Yahoo!, etc.) you will need to visit their websites to find out how to reset their passwords.

To retrieve or reset your email passwords, you will have to visit your email provider's website and attempt your login there, or click the password reset link there at their site(s).

If you are using High Sierra or older with AOL, you may need to create what's called an "application specific password". AOL thinks older software is less secure so you have a new hoop to jump through.

Create and manage third-party app passwords - AOL Help:

https://help.aol.com/articles/Create-and-manage-app-password

Hello,

Many eMail providers now require a separate App Password different from your eMail password…

Then you may need Ways to securely access AOL Mail…

https://help.aol.com/articles/allow-apps-that-use-less-secure-sign-in

Or it may just need an App Password...

https://support.google.com/mail/answer/185833?hl=en-GB

Yahoo has gone to this too...

https://help.yahoo.com/kb/access-yahoo-mail-third-party-apps-sln15241.html

Yahoo App password…

Generate and manage third-party app passwords

Some older, third-party email apps (that do not use our Yahoo branded sign in page) require you to enter a single password for login credentials. To access your Yahoo Mail account on these apps, you'll need to generate and use an app password. An app password is a long, randomly generated code that gives a non-Yahoo app permission to access your Yahoo account. You’ll only need to provide this code once to sign in to your third-party email app.

https://help.yahoo.com/kb/access-yahoo-mail-third-party-apps-sln15241.html

Using app passwords with apps that don't support two-step verification (microsoft.com)