The information professionals at the University of California at Berkeley recommend a graduated approach to Web searching [1]. Here's their stepwise sequence of steps to follow, which we generally endorse for beginning searchers:
 

As you gain experience, you can begin cutting out the middle steps. By the time you're doing real heavy lifting with your queries, you really only need spend some time first getting your query right and then cutting to the bottom line with a full Boolean search using phrases and three or so concepts linked through the AND operator and multiple search engines.

Here's a recap of some of the recommendations made throughout this tutorial:

• Spend time BEFORE your search to analyze what you're looking for
• Use nouns in your queries - the who/what, when, where, how and why; avoid conjunctions, verbs, adverbs and adjectives
• Use keywords at the right "level" of specificity: precise, but not overly restrictive
• Use phrases where natural; they are your most powerful weapon
• Use structured ("Boolean") syntax, especially the 'AND' operator
• Constrain your search by using two or three related, but narrowing, concepts in your query
• Keep overall query length limited to six to eight keywords
• Use advanced search options and specialty features when appropriate 
• Use multiple search engines for your most important queries - research shows accuracy improves many-fold. 
• For difficult searches, use only search engines that support Boolean syntax, or tools or metasearchers that do.
• For specific topic searches, use search engines tailored to those topics
• Save time by learning your search engines and power searching  techniques. 

Fondren Library at Rice University has also published useful tips on Internet search strategies [2].  For advanced topics, and a resource that is increasingly focusing on Web-related topics, you may want to consult Searcher:  The Magazine for Database Professionals [3]. 
 
 Finally, for issues relating to search engines, their capabilities, market share and how they work, two excellent resources are VirtualPromote [4] and Search Engine Watch [5].  You may also enjoy checking out Steve Steinberg's fascinating article for Wired on the nature of search services and the general topic of why knowledge organization matters [6]. 
 

Footnotes:
1 -- "Searching the World Wide Web:  Strategies, Analyzing Your Topic, Choosing Search Tools," issued by the Teaching Library Internet Workshops from UC Berkeley, found at:  http://www.lib.berkeley.edu/TeachingGuides/Internet/Strategies/html
2 -- See http://www.rice.edu/Fondren/Netguides/strategies.html.
3 -- See http://www.infotoday.com/searcher/srchrtop.htm.
4 -- One of the best discussions about metatags can be found on the Virtual Promote site: http://www.virtualpromote.com/metatag.html.
5 -- Search Engine Watch is a very useful, authoritative site on all aspects of search engines.  It is found at:  http://www.searchenginewatch.com.  Highly recommended.
6 -- The Steinberg article may be found at: http://www.wired.com/wired/archive/4.05/indexweb.html