If you take a look at the url of the search results page, you will notice that the search parameters are passed in using url variables like this:
searchpageurl.php?param1=product¶m2=value2&Search.x=1&Search=Search
Search.x is the x position on the button that is pressed, so you can leave it as 1. Search=Search specifies to do the search. param1 and param2 are different search parameters. In your case it seems you will only need to have one.