(Settings ➔ Apple ID(Top) ➔ iCloud on a mobile device and System Preferences ➔ iCloud on a Mac) However, whichever device you choose to move your data on, you should do so by turning individual iCloud services off one at a time and not sign out of the account until all services have been turned off and dealt with. Moving your iCloud data from one Apple ID to another is achieved more easily on a computer than it is on an iOS device, indeed certain aspects of the move can only be done on a computer. Be aware though that when using Family sharing, unless each family member has their own credit sum from iTunes gift vouchers, the organiser of the family share set up will pay for any purchases made by any family member. If the previous Apple ID is going to continue to be used by a family member who is part of a family sharing set up which will include your new Apple ID, you will be able to share the previous purchases as well as any further purchases they make under that Apple ID.
Whilst you won't lose apps you purchased using the previous Apple ID immediately, you will no longer be able to update them. If you do use your new Apple ID for the iTunes and App stores, you will be able to authorise and play previously purchased content from the iTunes Store on a computer, but may encounter difficulties using this content on an iOS device. You may want to think about continuing to use the previous Apple ID for the iTunes & App stores (as well as iBooks) so that you can continue to use your purchased content without a problem and just use the new Apple ID for iCloud, Messages and FaceTime. If you create and use a wholly new (not amended) Apple ID, you won’t be able to transfer anything you have purchased from the iTunes & App stores to the new ID, but you can transfer your iCloud data (calendars etc) with a little patience.