How do I set up a new Drupal instance with all the modules from a previous one? I had a temporary instance of drupal set up with lots of modules. I now have a new instance of Drupal and I want to install all the same modules, but I can only see how to do it with the GUI admin interface, which is frankly, horrifically clunky and unwieldy. 

Is there another way to do this without spending half a day manually installing them again?

I've only heard of Drush, but I'm not sure how to set this up on windows, so this might not be the best answer. Everything I search for online (e.g. 'Export drupal modules') points me back to a 'modules that exports nodes etc.', not a 'mechanism for exporting modules'.

I've also found something called Deploy but I can't tell if this is for modules or just nodes.
This is where the concept of drupal distributions comes in.

Yes you will need drush, a make file with the modules you need and a profile that installs these modules upon site-install.