Trap/Neuter-spay/Return (TNR) is undoubtably the most effective, most safe, and most compassionate solution to the feral and abandoned cat problems.  It is a humane process of catching, "fixing" and returning the cats to their "territory.   TNR can stabilize, and eventually reduce cat populations.  The 4 steps of TNR are Feed, Fast, Fix, & Friend. 

FEED  The TNR process starts with the trapper or colony caretaker placing a few layers of newspaper on the floor and cat food inside the humane trap. The trap should be zip-tied or blocked somehow so that the spring door does not close and the cat can freely go in and out.  The food is first placed in the front of the trap, and over time pushed to the back where it needs to be when the trap is set.  Eventually, when the cat seems comfortable going fully into the trap,  plans are made for "fixing" also known as "altering" or Spay/Neuter, safe and relatively painless surgeries   that make it so the cats will no longer re-produce.

FAST  Depending on  how skinny or fat the cat's are, and how much other food is available, the cats are not fed for 1-3 days.  Cats can live for 17 days without food, so one or two days without food is no hardship compared to the reduced quality and  quantity of life that an "un-altered" cat faces.

FIX After the "fast", the trap is "baited" with some yummy, higher than normal value food, like canned cat food, or tuna fish.  The "spring" is set.  Once trapped, the cat is kept in a safe and shaded place until it is transported to the doctor/clinic to be altered.
FRIEND   Usually the same day of surgery, the cat is ready to go home. Regardless of if the trapper will be a feeder/caretaker or if the cats will just be returned, it's best to keep the cats, especially the females inside or in a kitty condo for a day or two if possible, so they have a safe and quiet place to recover a bit.