how do i get my form to show up on random Facebook users homepages?

I'm not sure what exactly you are referring to display the form randomly. When the form is published on any of your webpages, it will be displayed everytime the page is loaded. Could you provide us with more information on your requirement so that we can guide you in the right direction.

Thank you!

I believe tsvevents' intention is to spam fb users using JotForm. Makes you wonder what type of information will be gathered.