For advanced searching, GoogleGuide.com has a great list of operators to limit your results. “Power Searching with Google” has a similar list. Western Kentucky University Libraries has a table of advanced search commands for Google and other search engines. Google also has its own basic and advanced search help pages. I recommend giving the “site:” command a spin.
Looking for Google’s latest and greatest? Try the company’s official blog.
Last but not least, take a look at Google 101 for Journalists.
And although it doesn’t fall under the category of “tips,” you might find the 2008 Atlantic article “Is Google Making Us Stupid?” interesting.