How do you move a device from one apple ID account to another?

You would need to sign out of the account in icloud settings, iTunes and App Stores, iMessage and Facetime on the device, and then sign in with the other account.

Sign in with a different Apple ID on your iPhone, iPad, or iPod touch - Apple Support

Note that all purchases and downloads made on one ID will remain tied to it forever, and in the case of Apps will require the Apple ID and password for it to update. In the case of iCloud, any extra storage bought remains with the Apple ID that bought it.

When you sign out of the iCloud account you are sharing, in Settings on your iPhone you will be asked whether you want to keep the contents on the iPhone or delete them.

Choose to keep them on the iPhone, then when you log in with the new iCloud Account, you will be asked if you wish to merge them to the new account. Answer yes, and your Calendar and Contacts should be part of the new account.

If your email account is not an iCloud email, then it is not affected by signing out and should remain on your iPhone.

If you were using the iCloud email from the shared iCloud account as your own, then you will need to manually forward the messages you wish to keep to the new account.

betsy.hight wrote:

I am trying to separate my email, contacts and calendar from my husband's account. We appear to be sharing the same iCloud.

The proper way to do this, once you have set up your own independent Apple ID, would be to erase the iPhone, and you take it over as if it were a brand new device being used for the first time.

Fundamentally, this means doing Settings > General > Reset > Erase All Content and Settings to the iPhone. But there is a bit more, which is documented here:

What to do before you sell or give away your iPhone, iPad, or iPod touch - Apple Support

No. Calendar, Contacts and iCloud email are tied to the iCloud account they are stored in.

Why do you need to move the iPhone to a new Apple ID?