How do I use the app-specific password to sing in

Note that the title to your post says "How do I use ..." and the body of the post says "how do I access ..." so it isn't clear to me exactly what it is that you are asking so the following may or may not help.

You put the Apple app-specific password into whatever 3rd party app that is needing a password to access iCloud. For example, if you are using a 3rd party email app (rather than the Apple Mail) app to access your iCloud email, you would put the app-specific password into that app wherever it needs the password for iCloud. Also see: Using app-specific passwords - Apple Support

So, I just got a new phone and would like to use the same third-party app for my mail client. I'd like to see my existing app-specific password for this specific app so that I can simply enter that already existing password into my new installation of this app which I have been using for years, rather than generate a new app specific password. How can I do this? How can I see what the existing app-specific password is?

How do you see the app specific password I created?

From the Apple Support FoxFifth posted.

1. Sign in to appleid.apple.com.
2. In the Sign-In and Security section, click App-Specific Passwords.