Normally once you have confirmed your booking, it should only take up to one minute to receive confirmation of the booking on-screen. A confirmation email will then be sent to the address you provided.
The email might go to your junk inbox - so do check there. As a precaution all the bookings are also stored online and can be accessed on this page. You will need your booking reference number and the email address you made your booking with to log in. You can reprint your confirmation email from there.
If you do not have the confirmation number of your booking you will need to contact Booking.com and they will re-send it for you:
+44 20 3320 2609
Please make sure that you list the name you made the booking for, the name of the hotel and your check-in and check-out dates.