In order to receive reservations you need to place the [wprm_booking_form] shortcode inside a page. You also need to make sure, you have selected that page into the booking settings page. Once a reservation is made, it will be saved into your manage reservations panel. From this panel, you can approve/reject/delete reservations.
Automatically Approve All Reservations:
WPRM has the option to automatically approve all reservations without the need to manually approve it from the backend. To enable this feature navigate to your restaurant settings page, select the "booking settings" tab, and switch the option "Booking Default Status" to "Automatically Approve Bookings".