<p>I want to create dynamic content based on this. I know it's somewhere, as web analytics engines can get this data to determine how people got to your site (referrer, search terms used, etc.), but I don't know how to get at it myself.</p>

You can use the "referer" part of the request that the user sent to figure out what he searched for. Example from Google:
http://www.google.no/search?q=stack%20overflow
So you must search the string (in ASP(.NET) this can be found be looking in
```
Request.Referer
```
) for "q=" and then URLDecode the contents.
Also, you should take a look at this article that talks more about referrers and also other methods to track your visitors:
http://www.15seconds.com/issue/021119.htm