As you can see in the picture above, Trivago is basically a search engine through booking sites.
So, there is no need to perform separate searches on Booking.com, Hotels.com, HRS.com and so on. Trivago will do it for you and will show you the rates offered by all those well-known booking sites.
For example, when searching for a 2 night stay in Luxembourg for the period January 22-24, 2010, the following results are returned:
Once you decided on the hotel, you just simply click on the link for booking site of your choice and then make the reservation.