If I create a custom post type with lots of custom fields,

If I create a custom post type with lots of custom fields, how do I modify the search field on the list page so that the search will include some of the custom fields?

For example, I have a custom post with a company name and a WP user associated with it. I want to be able to enter a partial company name and find similar companies and their users, or enter a partial user names, and see a list of users and the related companies.

I've already got the list display working the way I want it, but just need the search to work.