Transfer iPhone contents to iTunes
You can use iTunes that will transfer your old phone data to your Mac (and back to new phone)

or

You can use iCloud that will back up your old phone to iCloud (and back to new phone)

Do not forget the actual Phone function (the SIM card), use the old or use the new (if you got one).

Very specific instructions for all methods above are available from Apple here..

I personally prefer the iTunes to my Mac method.