1. The best way to begin searching harder with Google is by clicking the Advanced Search link.

2. This lets you search for exact phrases, "all these words", or one of the specified keywords by entering search terms into the appropriate box.

3. You can also define how many results you want on the page, what language and what file type you're looking for, all with menus.

4. Advanced Search lets you type in a Top Level Domain (like .co.uk) in the "Search within site of domain" box to restrict results.

5. And you can click the "Date, usage rights, numeric range and more" link to access more advanced features.

6. Save time – most of these advanced features are also available in Google's front page search box, as command line parameters.

7. Google's main search invisibly combines search terms with the Boolean construct "AND". When you enter smoke fire – it looks for smoke AND fire.

8. To make Google search for smoke or fire, just type smoke OR fire

9. Instead of OR you can type the | symbol, like this: smoke | fire

10. Boolean connectors like AND and OR are case sensitive. They must be upper case.

11. Search for a specific term, then one keyword OR another by grouping them with parentheses, like this: water (smoke OR fire)

12. To look for phrases, put them in quotes: "there's no smoke without fire"

13. Synonym search looks for words that mean similar things. Use the tilde symbol before your keyword, like this: ~eggplant

14. Exclude specific key words with the minus operator. new pram -ebayexcludes all results from eBay.

15. Common words, like I, and, then and if are ignored by Google. These are called "stop words".

16. The plus operator makes sure stop words are included. Like: fish +and chips

17. If a stop word is included in a phrase between quote marks as a phrase, the word is searched for.

18. You can also ask Google to fill in a blank. Try: Christopher Columbus discovered *

19. Search for a numerical range using the numrange operator. For example, search for Sony TV between £300 and £500 with the string Sony TV £300..£500

20. Google recognises 13 main file types through advanced search, including all Microsoft Office Document types, Lotus, PostScript, Shockwave Flash and plain text files.

full list via techradar.

5.  define: - Provides short definitions for words, acronyms, or common phrases.  

4.  address, city, state – A quick and dirty shortcut for mapping out a physical address using Google Maps. 

3. site: - Used for concentrating a Google search on a single website or domain name.  

2. filetype: - Filters a search result so that it only includes documents of a specific file format.  

1. allinanchor: - Conducts a search based on keywords used strictly in the anchor text, or linking text, of third party sites that link to the web pages returned by the Google search.  

via marcandangel