This is the essential parts of the 'source' for the basic search form extracted from the web page you indicated:
<form action="/search.php#results" method="post">
<strong>Basic Search </strong>
<strong>First Name:</strong><br> <input name="fFIRSTNAME" type="text" size="10" maxlength="25" value="">
<strong>Last Name:</strong><br> <input name="fLASTNAME" type="text" size="10" maxlength="25" value="">
</form>
The <form> tells you that the form data is sent to the server via post, and the <input>'s give the field names 'fFIRSTNAME' and 'fLASTNAME'
You then 'encode' the form data and post it to the server.
There's a pretty good article on how to do that here:
http://www.voidspace.org.uk/python/a.../urllib2.shtml