Where can I find instructions on how to insert keywords into my website based upon what someone was searching for? For example, if the person types in "flying pigs" and ends up clicking my link, I'd like to see the words, "flying pigs" in my title and throughout my website.

I'm not quite sure which search you're referring to, are you talking about an integrated search found in your website or a search engine like Google? If you're referring to something like Google, then creating a script that would do that would probably be considered black hat SEO as it could be considered cheating the system by creating such keywords automatically. If you're referring to the other thing I mentioned, unfortunately I'm not a PHP expert so I can't guide you through it but it should be possible, try looking at the search functions of some free blog/CMS scripts as they usually do that and you can try to modify that code to suit your needs.