Quotes: Anything you put in quotes ("") will search *only* for that exact phrase (and spelling). Try googling for: "how I wonder what you are" with and without the quotes. See how much better the results were if you were looking for the lyrics to Twinkle Twinkle Little Star?
Proper Sentences Not Required: You don't have to search for specific phrases. Think of a group of related words, such as: funny kitty cat photo picture video
Required terms: If you want to only have results that talk about youtube, then add + to your term in the search box. Try: funny kitty cat photo picture video +youtube
Excluded terms: You can exclude results that list a term as well with a minus. Try: funny kitty cat photo picture video -youtube
Searching your favorite website: If you only want results from a specific website, then add site: to your searchbox. Try: funny kitty cat photo picture video site:youtube.com . Try it again with site:ebay.com to see how it changes your results.
I didn't realize Google could use synonyms. A quick google for "google tips and tricks" told me about it though. Searching for ~cat will also search for kitten, feline, and other synonyms.
Calculator: If you can't find one, let google do it for you! Try: 45 + 83 / 2
Maps.google.com trick: The to: and from: are very important though. Try: from: chicago, il to: st. louis, mo . My favorite maps trick is when I have more than one stop. Try: from: 3720 green mount crossing drive shiloh il to: chicago il to: indianapolis in