Alexa home search:
<form id="searchBox_form" class="searchForm" action='http://www.alexa.com/search' onsubmit="$.cookie('ax_gr_last_tab', '#trafficstats', { expires: 1});">
<!-- source: http://www.wiibeez.com --><div class="query"><input name="q" type="text" title="Enter a search query" value="" class="ac_input" id="searchbox" size="55"/></div>
<button type="submit" ><span>Search</span></button>
<input type="hidden" name="r" value="home_home" />
<input type="hidden" name="p" value="bigtop" />
</form>

Alexa top sites search:
<form id="searchBox_form" class="searchForm" action='http://www.alexa.com/search' onsubmit="$.cookie('ax_gr_last_tab', '#trafficstats', { expires: 1});">
<!-- source: http://www.wiibeez.com --><div class="query"><input name="q" type="text" title="Enter a search query" value="" class="ac_input" id="searchbox" size="30"/></div>
<button type="submit" ><span>Search</span></button>
<input type="hidden" name="r" value="topsites_index" />
<input type="hidden" name="p" value="bigtop" />
</form>

Alexa site info search:
<form id="searchBox_form" class="searchForm" action='http://www.alexa.com/search' onsubmit="$.cookie('ax_gr_last_tab', '#trafficstats', { expires: 1});">
<!-- source: http://www.wiibeez.com --><div class="query"><input name="q" type="text" title="Enter a search query" value="" class="ac_input" id="searchbox" size="30"/></div>
<button type="submit" ><span>Search</span></button>
<input type="hidden" name="r" value="site_siteinfo" />
<input type="hidden" name="p" value="bigtop" />
</form>

Alexa What's hot search:
<form id="hot-search" action="http://www.alexa.com/whatshot" class="searchForm">
<!-- source: http://www.wiibeez.com --><div class="query"><input type="text" name="q" value="" class="ac_input"/></div>
<button type="submit" ><span>Search</span></button>
</form>

Perform a search on the selected site you want to get the search source code, and check result URL, must be like: http://www.site.com/search , or ending with: /search2.php or /Tsearch or /form_search.php ... ..., just replace in the form code the url search ending.

Or just the url on the search form  <form action="http://www.site.com" ending with this tag: method="get">

 If you have more than one search box in one webpage, and if you want to keep the showing text inside the search box everytimes from one to another search box, add the following tag: onfocus="if(this.value==this.defaultValue)this.value='';" onblur="if(this.value=='')this.value=this.defaultValue;"
EXEMPLE: <input type="text" name="q" id="srch_bx" value="Search multi-results" onfocus="if(this.value==this.defaultValue)this.value='';" onblur="if(this.value=='')this.value=this.defaultValue;" autocomplete="off" size="35"/> into the "<input type=... ...> tag.

To open the search results in a new window, use the target="_blank" tag,
exemple for youtube:
<form id="vb_yt_search-form" action="http://www.youtube.com/results" method="get" target="_blank">
<p align="center">
</p>
<p align="left">
<input id="vb_yt_search-term" name="search_query" type="text" maxlength="128" size="30" /> <input type="submit" value="Search Youtube" />
</p>
</form>

This tag will open the youtube search results in a new window. Add this tag after the tag <form name="" or after the tag method="get".To get the results in the same window, simply remove the target="_blank" tag.

Add an image inside the script code, so the image fit correctly with the search box. Add your image tag after the <form... ... action="http://www.sitename.com/search">
exemple:
<form name="f" target="_blank" style="margin-bottom: 20px" action="http://www.google.com/search">
<p align="center">
<img border="0" src="yourlogo.gif" width="400" height="180">...........up to end of script.......... form/>.

For other search form type. Add your text and images after the <ins> tag and add the <br> tag just after. Exemple here:
FROM THIS:
<form action="http://SITE.com/THEME_search.php" method="get" target="_blank" id="search" onSubmit="return ms_check();">
<ins>
<input name="q" id="search_q" size="25" style="background-color: #F5F5F5" /></ins>
<ins>
<input type="submit" value="Search" class="button" class="searchbutton"></ins>
</form>

TO THIS:
<form action="http://SITE.com/THEME_search.php" method="get" target="_blank" id="search" onSubmit="return ms_check();">
<ins>
<img border="0" src="IMAGE.gif"><b><font face="Verdana">Search
<font size="4" color="#000080">10starmovies.com</font></font></b><br>
<input name="q" id="search_q" size="25" style="background-color: #F5F5F5" /></ins>
<ins>
<input type="submit" value="Search" class="button" class="searchbutton"></ins>
</form>

Modify the size of the search box by using the size="" tag. Add this tag after the maxlength="" tag
exemple:
<form method="get" action="http://search.ebay.com/search/search.dll">
<input type="hidden" name="fts" value="2" />
<input type="text" name="satitle" value="" maxlength="300" size="50" />
<input type="submit" value="Search Ebay" />
</form>

Worldwide web: