I have just built my own website and would like to submit my website to
various search engines, such as Google and Yahoo. Can you please tell me
how
to define the text that the search result shows?
The search results normally show the meta description tag text.
Right-click and select 'Page Properties', then enter the description for the
page you want to use.
Although some people use the same description on every page (a general
description for the site) it's better to have a separate description for
every page, which improves the way the SE's pick up multiple pages on the
site.
The other thing worth doing is to create an account on Google Webmaster
Tools,
https://www.google.com/webmasters/tools/docs/en/about.html and using
the various tools they offer.