Navigate to your reservations management panel, here you will see a list of all your bookings. If you wish to approve a booking, simply hover with your mouse on the reservation and a list of links will appear. One of the links is "approve", by pressing the approve button, the reservation will be approved and if enabled, a mail notification will be sent.
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".