How do I delete an Apple ID that I am no longer using?

By "Delete" do you mean just sign out of it from your devices, or do you mean you want to erase the Apple ID from existence entirely?

If you just wish to sign out of it from a particular device, go to the following locations:

Settings ➜ Apple ID (scroll to the bottom, and select Sign out)

Settings ➜ Apple ID ➜ Media & Purchases ➜ Sign Out

Settings ➜ Messages ➜ Send & Receive ➜ Apple ID ➜ Sign Out

Settings ➜ FaceTime ➜ Apple ID ➜ Sign Out.

If you really want to completely erase the Apple ID from existence, then make sure you sign out as above on every device that is still using the Apple ID in question and read below:

Do note, any apps, movies, TV shows or books purchased or downloaded with the Apple ID are forever tied to the Apple ID and will stop working or being accessible if you completely erase the Apple ID from existence.

Make sure you have erased all these apps, movies and shows from your devices before requesting deletion.

Any data, files, music, or photos in the iCloud account associated with the Apple ID will no longer be accessible.

Also as already mentioned make absolutely sure Apple devices using said Apple ID have been logged out of it, as otherwise they may be rendered unusable if you complete the erasure process.

Erasing an Apple ID is not reversible. Make absolutely sure you never want to use the Apple ID again for any reason as you will not have access to it ever again once its completely erased.

click here ➜ How to delete your Apple ID account - Apple Support