If you are moving to the same type of phone, use iCloud, your Google account or Microsoft account (depending on which type of phone it is) to back up your current device. (For a how-to, visit goodhousekeeping.co.uk/back-up-your-smartphone).
Switch the new device on to be walked through the steps for setting it up. When you come to the screen that asks you if you have an Apple ID, a Google or Microsoft account (again depending on the type of phone you have) enter the account details and make sure youselect the option that says 'Restore from last back up of this account'.
To move contacts between different makes of phone, see goodhousekeeping.co.uk/how-to-move-contacts.
Feature in Good Housekeeping, September 2016
I was always making notes on scraps of paper about tips and facts I'd read in books and magazines, seen on the Internet or on TV. So this is my paperless filing system for all those bits of information I want to access easily. (Please note: I live in the UK, so any financial or legal information relates only to the UK.)