I wrote this StackOverflow answer, explaining how you can safely backup your work, destroy the old PHP 5.6 Vagrant box and download a brand new one that comes with PHP 7 as standard.
In my opinion this will be easier and cleaner for most people than trying to perform an in-place upgrade (the exception is where you’ve extensively customised PHP, MySQL or Nginx, in which case you need to backup the appropriate config files too.)
There are also some notes on the format of Homestead.yaml when you have more than one site, as the documentation on shared folders isn’t terribly clear.