In the first two investigations of To Catch a Predator, Dateline/Perverted Justice were acting alone to out (and hopefully deter) potential predators. From then on, local police became interested in doing a side-by-side investigation with cooperation; they would temporarily deputise the Perverted Justice crew in exchange for all evidence collected (such as computer chat logs, photos and phone calls).
The role of the sting operation for these predators is the same as a sting operation for trying to catch drug dealers. They setup the scenario as if it real, making sure to have as much evidence of intent as possible to demonstrate to the judge that the predator was, beyond reasonable doubt, interested in committing a real felonious act. This is why the predators are often asked to bring certain items; the more things they bring in, the more proof police have of the potential for a criminal act which may have taken place.
The predators are always charged with various "attempts", as obviously they weren't actually caught in the act. It should be noted that many of the paedophiles that are caught on the show have an extensive history of child love crimes, and are usually known to police. Some were even awaiting court dates for previous criminal acts when they arrived at the house.
The original run was partly canned thanks to one creep, Louis Conradt, Jr. (Assistant District Attorney). This ballsy forgeter was coming from another county, but he never even got to the house. After he stopped communicating with the decoy (not before he had sent pictures of his snake and had explicit communication with somebody he knew to be underage), the investigating police got permission from the local police, at which point they attempted to arrest the forgeter in his home, but he killed himself to prevent capture (right as a SWAT team had found him).
