License for multiple domains
From what I understand you can use the one licence key on multiple
  environments but you can only then login to the Admin area from one of
  them?


Sort of – you'll be able to login everywhere, but if the license isn't valid the CP will be blocked behind a "upgrade-wall", prompting you to purchase a valid license or downgrading to Personal (the free edition). The frontend will continue to function as normal, though.


  Alternatively I can use Craft for 'Free' using a appropriate .dev or
  staging URL (eg. http://staging-subdomain.mysite.com) and then make
  sure the paid for license is in place on the live version. Is that
  correct?


Yes. From the docs:


  You’re allowed to run a single Craft license on multiple domains (e.g.
  example.com and example.fr), so long as they’re all a part of the same
  website. In order to enforce that, Craft does have one technical
  limitation: you may only access Craft’s control panel from one public
  domain per Craft license. (There is no such restriction on non-public
  domains, though.)


One of the ways Craft determines if the domain is non-public, is if the site has a dev-sounding sub domain (e.g. dev, local, stage, or staging). This means that a Client or Pro license registered to www.mysite.com should also work for a staging site at http://stage.mysite.com.