You can use Google's Advanced Search to formulate effective grey literature searches.
Often a website's search function fails to discover the results you might expect to find. Using Google's site or domain option to search within the website e.g., .gov.au may allow you to discover documents you're looking for.
Grey literature is often published online as a pdf or word document. Using Google's file type search will help narrow down the results to these file types.
Using Operators in your searches
Google allows you to use operators within your search to help you refine your searches. Some common ones include
+ for AND
- for NOT
OR for OR
"" for a phrase search
You'll find other refinement options here.
Google will display results based on your search history, preferences and website visits. You can use Verbatim mode in the tools option to disable this default function.
Internet search engines will provide access to material currently available online. When a website is taken down or the content owner changes - e.g., Government Departments, the content on these websites can disappear. Internet Archives are collections of archived websites that may provide you with access to some grey literature which is no longer available through a search engine.
Australian Internet Archives
Pandora - a growing collection of Australian online publications, established initially by the National Library of Australia in 1996.
Australian Government Web Archive - a collection of Commonwealth Government websites. Initially content collected specifically for the collection commenced in June 2011, content from before this time is gradually being added.
International Internet Archives
While much of the content you'll find in Google Scholar is not grey literature, the information comes from academic publishers, professional societies and university repositories, it does include
Haddaway, N. R., Collins, A. M., Coughlin, D., & Kirk, S. (2015). The Role of Google Scholar in Evidence Reviews and Its Applicability to Grey Literature Searching. Plos ONE, 10(9), 1-17. doi:10.1371/journal.pone.0138237
BASE index the metadata academically relevant resources - journals, institutional repositories, digital collections.