Grey literature is not easy to find, which is why it's "grey"! Expect to have to do quite a bit of searching. That being said, with more and more information being published online, it's become a bit easier.
Government agencies, research institutes, organizations, companies or associations will often have a link to "research" or "publications" on their website. If the body produces a large quantity of publications, then they might even have a "database" or "institutional repository" available for searching.
It is helpful if you know which bodies publish in your area of research interest, but if you don't know where to look, you have a few options:
These are just a few of the more general sources for grey literature. To see if there might be something specific to your research or program area, contact a librarian.