[Victor D]

I think this particular question is worth to be a separate thread.
open your customer/head.tpl
find this

    <div class="search">
      <div class="valign-middle">
        <form method="post" action="search.php" name="productsearchform">

          <input type="hidden" name="simple_search" value="Y" />
          <input type="hidden" name="mode" value="search" />
          <input type="hidden" name="posted_data[by_title]" value="Y" />
          <input type="hidden" name="posted_data[by_descr]" value="Y" />
          <input type="hidden" name="posted_data[by_sku]" value="Y" />
          <input type="hidden" name="posted_data[search_in_subcategories]" value="Y" />
          <input type="hidden" name="posted_data[including]" value="all" />

          {strip}

            <span class="search">{$lng.lbl_search}:</span>
            <input type="text" name="posted_data[substring]" size="16" value="{$search_prefilled.substring|escape}" />
            {include file="customer/buttons/button.tpl" type="input" style="image"}
            <a href="search.php" class="search">{$lng.lbl_advanced_search}</a>
          {/strip}

        </form>

      </div>
    </div>

copy it into new file customer/search.tpl and replace with
{include file="customer/search.tpl"}
and use it to include search box on the page.