Generate the html form can be done in Salesforce by an admin through your setup menu under Web-to-case HTML Generator.
Now you can simply copy/paste the code to your website but you might need someone who understand coding to adapt the style and/or doing some data validation etc.
The code generated will look like this :
<META HTTP-EQUIV="Content-type" CONTENT="text/html; charset=UTF-8">
<!-- ---------------------------------------------------------------------- -->
<!-- NOTE: Please add the following <FORM> element to your page. -->
<!-- ---------------------------------------------------------------------- -->
<form action="https://salesforce_instance" method="POST">
<input type=hidden name="orgid" value="org_id">
<input type=hidden name="retURL" value="http://your website url">
<!-- ---------------------------------------------------------------------- -->
<!-- NOTE: These fields are optional debugging elements. Please uncomment -->
<!-- these lines if you wish to test in debug mode. -->
<!-- <input type="hidden" name="debug" value=1> -->
<!-- <input type="hidden" name="debugEmail" -->
<!-- value="[email protected]"> -->
<!-- ---------------------------------------------------------------------- -->
<label for="name">Contact Name</label><input id="name" maxlength="80" name="name" size="20" type="text" /><br>
<label for="email">Email</label><input id="email" maxlength="80" name="email" size="20" type="text" /><br>
<label for="phone">Phone</label><input id="phone" maxlength="40" name="phone" size="20" type="text" /><br>
<label for="subject">Subject</label><input id="subject" maxlength="80" name="subject" size="20" type="text" /><br>
<label for="description">Description</label><textarea name="description"></textarea><br>
<input type="hidden" id="external" name="external" value="1" /><br>
<input type="submit" name="submit">
</form>