The steps to change your Apple ID are listed in this article:

It is recommended that you sign out of all your devices apart from the device you're using to change your Apple ID (I'd recommend using your laptop to make the changes). However, if you'd like to use your phone, here's a guide on how to sign out of your Apple ID on your phone

Sign out of all devices

You can log out of your devices individually or log in to to view the devices you're signed in to and manage them from there. If there are devices listed that you don't recognize or don't have access to (old devices perhaps) then you can click on the device and select 'Remove from Account'.

Once you've done that, at the top of this page you'll see the account section. Select 'Edit' and then 'Change Apple ID'. You'll be sent an email confirmation to your new email account to verify the changes and then you're done! Sign back into iCloud on your phone using the new Apple ID.