How do I change the iCloud/Apple ID on my iPhone? It is gray and will not allow me to edit it.

If you change your email, you do not need to "change" your AppleID. Just edit your email(s) on your Apple ID by logging in to your AppleID account. You should always use the same AppleID for Apple Services (iCloud, iTunes etc) and multiple ID will cause problems and confusion in the future.

You can manage your Apple ID here:

https://appleid.apple.com

First on the iPhone, Settings > iCloud and delete the account.

Then update your AppleID account as FelipeV suggested above.

Then re-add Settings > iCloud - Account.

See: Change your Apple ID