How do I delete or change my primary Apple ID?

See this help page:

Manage your Apple ID primary, rescue, alternate, and notification email addresses - Apple Support

And: Apple ID: What to do after you change your Apple ID

Go to system preference > iCloud then you can manage your Apple ID.

If your primary address (the ID) is an @icloud.com, @me.com or @mac.com address you cannot change it. If it is a non-Apple address you can change it as follows:

1. Firstly, if you have 'Find My iPhone/iPad/iMac' enabled on any of your devices, turn it off. (This is vital but for some reason the Apple Help page linked to above doesn't mention it.)
2. Create a new email address, for example at Yahoo or Gmail, or anywhere convenient (or you can use an existing address as long as it has never been associated with an Apple ID).
3. Go to http://appleid.apple.com and click 'Manage your Apple ID'. Sign in with the current ID.
4. Where it says 'Apple ID and primary email address' and gives your current ID email address, click 'edit'.
5. Enter your new address and click 'Save changes'.
6. Now you will need to go to each of your devices and sign out in System Preferences (or Settings)>iCloud - 'Sign out' on a Mac, 'Delete this account' on an iOS device (this will not delete the account from the server).
7. Then sign back in with your new ID. Your iCloud data will disappear from your devices when you sign out, but reappear when you sign back in.

I re-iterate: before you start, turn off 'Find My Mac' (or whatever) or you will need the services of Support.