I'd like to create a search box that only searches my site.

What code do I use?

Also, is there a way to have "common searches" come in a drop down box under the search as someone is typing, sort of like an auto-complete (similar to google)

Thanks for the direction

Download Windows Freeware and shareware - Tucows is a link to freeware/shareware search engines that you can download and use on your web site. All come with different features and are documented for your customizations. General individual browser settings determine command line/text completion for forms although there is also something called "search engine query log mining" which when used will allow your search engine to make recommendations on queries based on previous queries. Again, this is a feature you would have to look for and enable on one of the aforementioned out of the box solutions.