I want to add a simple Contact form to my web site so that customers can contact me easily.
If you want to do a completely front-end solution I have had success recently by leaving the form action attribute blank, and populating it via a $(document).ready function. Most spambots use a browser that has javascript disabled, or are looking for hidden fields to avoid detection.
Example:
Your html would be:
and anywhere in that page you can use this to populate it.
A bot browser with no javascript will not get a form action, and they will get a 404 upon submission. Anyone with a normal browser (unless they have JS disabled for paranoid reasons) will get the normal behavior.