Its actually quite straight forward. Let me try to explain it.
You create a basic HTML form and place a input form field for your search box and a button like so:
<label for="keywords">Search:</label>
<input type="text" name="keywords" id="keywords" value="" size="18" maxlength="100" />
<input type="submit" value="submit" class="submit" />
Then, for a simple search, you wrap it in EE tags:
{exp:search:simple_form weblog="news"}
<label for="keywords">Search:</label>
<input type="text" name="keywords" id="keywords" value="" size="18" maxlength="100" />
<input type="submit" value="submit" class="submit" />
{/exp:search:simple_form}
and BAM! you have a simple search form. Just change the weblog parm in the search:simple_form tag to which ever weblog you want to search or remove weblog param and add this to search everywhere:
{exp:search:simple_form ... search_in="everywhere"}
Here is a complete listing of search parameters.
Additionally, you can indicate a specific template where you want your search results to appear. Note the “search_results” parameter.
By default your EE install comes with a pre-formated “Results” template in your “Search” template group.
Hope this helps.