Basically, the degree of customization of your booking engine depends on your provider. You can integrate the booking engine into your hotel website using a simple "Book" button or a more elaborate interface.
When installing your booking engine, your provider or site developer will adapt its style to your site's fonts and colors to match the look and feel of your hotel's site.
With most providers you can also customize most of the fields in your booking engine, such as the maximum number of travelers, the thank you message, or the information required to make the reservation.