To perform an advanced Google search, click the gear icon to specify search filters like domain, reading level, or file type. This allows searching specific websites, like .edu or .org domains, or finding documents in formats like PDFs or PowerPoints. Placing a * in the search bar acts as a wildcard to find information when a term is missing. Additionally, directly searching website domains like pbs.org or history.com can yield better results than those sites' internal search functions.