-Parts of a Search Engine:

Search engines consist of 3 main parts. Search engine spiders follow links on the web to request pages that are either not yet indexed or have been updated since they were last indexed. These pages are crawled and are added to the search engine index (also known as the catalog). When you search using a major search engine you are not actually searching the web, but are searching a slightly outdated index of content which roughly represents the content of the web. The third part of a search engine is the search interface and relevancy software. For each search query search engines typically do most or all of the following
Accept the user inputted query, checking to match any advanced syntax and checking to see if the query is misspelled to recommend more popular or correct spelling variations.
Check to see if the query is relevant to other vertical search databases (such as news search or product search) and place relevant links to a few items from that type of search query near the regular search results.
Gather a list of relevant pages for the organic search results. These results are ranked based on page content, usage data, and link citation data.
Request a list of relevant ads to place near the search results.
Searchers generally tend to click mostly on the top few search results, as noted in this article by Jakob Nielsen, and backed up by this search result eye tracking study.
Want to learn more about how search engines work?
In How does Google collect and rank results? Google engineer Matt Cutts briefly discusses how Google works.
Google engineer Jeff Dean lectures a University of Washington class on how a search query at Google works in this video.
The Chicago Tribune ran a special piece titled Gunning for Google, including around a dozen audio interviews, 3 columns, and this graphic about how Google works.
How Stuff Works covers search engines in How Internet Search Engines Work.