The easiest way is to add first a calendar plugin to your WordPress site. Then you use the direct Hostaway iCal export links to show your users per listing what dates are available. Adding a nice Booking button per page redirecting to your Hostaway booking website will do the rest.
If you are a programmer we might have some options for you by API to integrate in to your WP website. For more information about this option you can contact support.
If you are looking for a fully functional WordPress? Send you request to support and we contact you when our WordPress booking module is ready.