Creating a node with multiple joined fields I'm sure I used to know how to do this, but now I can't work it out. 

I have a content type, lets say it's called "project". A project can have multiple contributors, and for each contributor I need to have two fields, let's say "Name" and "University". Can I set this up as a single Content type? 

If not (and I have to have a Content type for the project and a Content type for the contributor, using entity reference to link them), then how do I set it up so it's easy to edit on a single page (i.e. create a new project, click something to add another contributor on the same page)
I'd recommend keeping the contributors separate with their own fields. In order to edit them on the one form you can use a number of different modules. We use Inline Entity form.
https://www.drupal.org/project/inline_entity_form