Filtering search using checkboxes

I have a form that allows users to search my website. The site has different sections, each one corresponding to a custom post type (it's based on Wordpress), so I've added a filter where the user can check in which of the sections they want to search.

How can I detect which checkboxes have been ticked so that when the results page is loaded they are correctly filtered? Can I do it with $_POST or do I need a cookie?

I'm sure this is pretty simple but I have little experience with forms and posting values, so I need a little direction. Thank you for your help!