The answer depends on what you are doing exactly. If the user selects an option and the results are shown on a new page, the data would be submitted in a form. The form can be submitted by query using the 'change' event.
<form action='#' method='get' />
<select name='company size'>
If the data is shown on the same page, the process is basically the same, except you would use Ajax to submit and retrieve the form data.
You would then use wp_query to search for posts that match the variable.