TripExpert is using expedia's affiliate program. You can signup as an affiliate in a few minutes. They give you a link that takes your users to expedia's site to complete the booking. You get a small percentage of the bookings made via your link.
Hotel.com which is owned by expedia connects to hotels via a Global Distribution System (GDS) like Sabre or Pegasus. All reasonable sized hotel's connect to one of the GDS's (there are 3-4) and travel agents and OTA's like expedia and priceline also connect to them. Getting access to one of the GDS systems takes time and costs a lot. The GDS's speak XML using the Open Travel Alliance's spec. Travel agents typically make a 10% commission on books they make. Hotels pay the commission to the TA and usually a couple of dollars per booking to the GDS. Expedia and the other big OTA's do it differently, making deals with each hotel company and charge much higher commissions.