How do I set up a new Apple ID and delete my old one?

This document will show you how to create a new Apple ID (create an Apple Account) --> How to create a new Apple ID - Apple Support

For information about how to delete your Apple ID account, click here --> How to delete your Apple ID account - Apple Support

The thing is, all that is rather extreme unless you have a good reason for doing it. For starters, anything purchased with one account is permanently tied to it and will be lost with a new account, particularly if you delete the old account.

Maybe you mean instead to simply change the email address?

Here's how you change the email address you use for your Apple ID:

1. Go to https://appleid.apple.com and sign in.

2. In the Sign-In and Security section, choose Apple ID.

3. Enter the email address that you want to use as your Apple ID.

4. Choose Change Apple ID.

5. If you changed your Apple ID to a third-party email address, check your email for a verification code, then enter the code. Learn what to do if you didn't get the email. --> If you didn't receive your verification or reset email - Apple Support

6. If you use services like iCloud or Messages to share with friends and colleagues, sign in to those services with your updated Apple ID. --> What to do after you change your Apple ID or password - Apple Support

For more details, and how to do this if you have a mobile number ID, see the document Change your Apple ID - Change your Apple ID - Apple Support