Zyb: export / copy mobile phone contacts to Gmail / other phone - howto & review

This post is part review, part howto guide, on:
how to copy or import your mobile phone contact numbers into Google’s Gmail contacts, if you have a Gmail / Google Mail account, and

whether you have Gmail or not, how to easily backup or transfer your contacts between different phones, e.g. if you’re moving networks (as your old SIM card will die when your current phone number is transferred