Do you remember a few years ago when Google sued dictionaries for including "google" as a verb? Whether or not Google approves, we all use the word to refer to searching on the Internet. But just because we know how to type words into a search box, this doesn't mean we know how to Google.

The Basics

AND - usually Google automatically searches for all of the terms you list

OR - you can use the | sign to tell google to search for one term or another

NOT - put a minus sign in front of the word you don't want to appear in your results

ALL - put the phrase you're looking for in quotes

Useful

SIMILAR - looking for something that's almost but not quite the word you have? use the ~ sign before it.

WILDCARD - The * is the wild card, use it to replace any word you're not sure of 

Narrow down your search further

define: - if you want to look for dictionary definitions of a word

filetype: - if you're looking for a specific document eg a spreadsheet (filetype:xls)

site: - if you want to search a specific site

link: - if you want to see all the sites that link to a specific site (eg your blog ;))

music: - returns content related to music only

movies: - put in your location and Google should bring up show times, however as far as I know this only works in the states :(

inurl:/intext:/inanchor: - search specific parts of a site

related: looks for similar sites

numrange - search within a range of numbers or dates by putting .. in between the two numbers

Other stuff Google can do:

calculations - put in a sum using / (for divide) and * (for times) to use Google as a calculater

conversion - Google can convert units and measurements. Eg inches in cm

the answer to life the universe and everything - Google knows

Read more

More information:

A great summary

More advanced stuff from the Google Guide