Help moving a backup of wordpress

Hi,

I have recently terminated my site hosting and managed to get a backup copy of the site in a zip file with all the database and other files necessary. I have signed up for a free .wordpress.com account but for the life of me do not even know where to start trying to restore the site. If that is even possible. All support I have read seems based on access to ftp or db which I don’t think I have access.

Can anyone shed some light on the subject, please?