Since Grey Literature isn't usually found in traditional databases (such as MEDLINE or CINAHL), you need to broaden your scope and consider other sources. Even Google Scholar won't include many grey sources, so depending on your topic of interest, explore other options such as the below tabbed grouping:
Comprehensive, multidisciplinary index providing bibliographic information for theses and dissertations from thousands of universities.
Provides access to research articles made available before the formal publication in a journal (preprints) from arXiv, bioRxiv, chemRxiv, medRxiv and Preprints.org respositories. Added functionality available with personal account.
Conducting a Web search and limiting to "site:.gov" can be a good way to start looking for governmentally-produced gray literature. However, it's good to have some of these sites already on your radar.