Humane traps like pictured here are used to catch the feral cats. Food is set just past a pressure plate, the cat will go inside the trap and trigger the door to shut. This is the safest and most humane way to catch ferals. Once trapped the trap is then covered with a blanket, not only to protect the carrier from scratches but to calm the cat.
The cats are then transported to a vet where they are spayed/neutered, given rabies, tested for FIV/FIP, treated for any illness or injury, and ear tipped. Ear tipping like shown in the picture is done while the cats are under anesthesia and is a way to identify cats that have already been vetted. This helps not to catch the same cats.
Once the cats are fully awake from surgery they are then returned to the location they were trapped. And under the care of a "Colony Caretaker" they are released. A Colony Caretaker ensures the colony has food, shelter, and if ever needed medical attention. Caretakers are crucial for a successful TNR!