The HTML of the form is the easy part, the more complex part is the form action which is the script that processes the form and saves it to a database or emails or what have you, you can find free processing forms on the web like http://www.freeforms.org/
the HTML is pretty simple for the form
<form name='petition' method='post' action='/' class='petition'>
Name:<br/>
<input type='text' name='petition_name' value=''/><br/>
E-mail address:<br/>
<input type='text' name='petition_email' value=''/><br/>
Postcode:<br/><input type='text' name='Postcode'/><br/>
Do not display name on website: <input type='checkbox' name='petition_keep_private'/><br
<input type='submit' name='Submit' value='Sign the petition'/>
</form>