Google's search process involves crawling websites to index their content, calculating the relevancy of pages using algorithms, and providing search results to users. Crawling involves Googlebot discovering and fetching pages to add to Google's index by following links. During indexing, words on pages are analyzed and pages are assigned to keywords. Relevancy is determined through ranking factors in algorithms that analyze search queries and results. Search aims to return the most useful and relevant information to users quickly based on their location, history, and context.