Magento generic form
https://magento.stackexchange.com/questions/130737/how-to-show-simple-calatog-search-form-on-cms-page
<form id="search_mini_form_cms" action="<?php echo Mage::getBaseUrl(Mage_Core_Model_Store::URL_TYPE_WEB); ?>index.php/catalogsearch/result/" method="get">
<div class="input-box">
<input id="search_cms" type="search" name="q" value="" class="input-text required-entry" maxlength="128" placeholder="Search entire store here..." autocomplete="off">
<button type="submit" title="Search" class="button search-button"><span><span>Search</span></span></button>
</div>
<div id="search_cms_autocomplete" class="search-autocomplete" style="display: none;"></div>
<script type="text/javascript">
//<![CDATA[
var cmsSearchForm = new Varien.searchForm('search_mini_form_cms', 'search_cms', '');
cmsSearchForm.initAutocomplete('{{store url='catalogsearch/ajax/suggest'}}', 'search_cms_autocomplete');
//]]>
</script>
</form>