To be sure that your own Web site appears in searches, you should register it with the search enginges. Most allow you to do that. But beware, you'll be getting more junk email than before. Many search engines transmogrified into portals in the past couple of years.
Portals pre-select the Web sites they display.
Some even write their own pages. The portals say they save us time by screening and rejecting large numbers of irrelevant sites. Note that, in August 1999, studies reported that only a small percentage of the Web was being indexed by search engines. Things may have improved since then. Also, some of these sites sell positions in their searches.