Well I am not a theme developer, so I am not familiar with the all of the details, but as far as I know the search.php theme file should be handling the search results.
I would probably start by taking a look at a sample theme, which has an implemented search.php file, and go from there. There should be a basic posts loop there for sure to handle the results, that I know. Unfortuantely I am no expert with theme development and inner workings.