My neighborhood used to be over run with feral cats. A few months ago two ladies started catching them, spaying and neutering them, and then finding homes for the friendly ones and releasing the really wild ones.
The way they catch them is baby simple. They have a large box which they prop up on a stick. There is a string tied to the stick about 30 feet long. They put food under the box and wait for the cat to go under to eat the food. Then they pull the string, and the box drops, trapping the cat. Next you slide some thin piece of plywood under the box to close off the bottom. The whole thing can be lifted by two people onto a vehicle, and the cat driven away to wherever you want to take it. They have caught about 15 cats this way, and now it's very rare to see a feral cat around here anymore.
The large box they use is actually just a frame made of 1 x 2 and covered with window screen. It's fairly light. I'd say it's about four feet square. They generally do their cat trapping between 11 PM and 2 AM.