Hi Jenn and WELCOME
We've been TNRing for around 6 years now and it really works well! Here's some pointers I can give you:

Do not feed cats for 24 to 48 hours before you trap them. They will go into the traps much easier when hungry!

Set the traps around the area the cats are use to being fed. Always use humane traps!

Put newspaper, folded in half length wise, in the bottom of the trap andput a small amount of smelly food on a lid or other small item in the back of the trap against the door that will remain closed. Sprinkle a very small amount of food along the newspaper with some juice. Never put food outside the trap itself.

Once cat is in trap immediatley cover the trap with a towel or sheet then take the cat away from the area. It could take the other cats a while to come back to the area so be patient.

Put the trapped cat somewhere where it will not be to adversely affected by weather and where it will be safe from people or other animals. Leave cover on trap the entire time the cat is in the trap. If the cat pulls the cover into the trap, just get another one and cover again.

Hold the cat overnight before releasing to ensure all anesthesia has worn off. Make sure they're in an area where they are safe from predators and protected from the elements. After surgery cats cannot regulate their body temperatures the way they normally can, so their holding area cannot be too cold in winter or too warm in summer. If there is continuing bleeding or other problems do not release cat. When you do release take the cat to its usual secure location preferably where there are bushes or other things in which it can hide. If the area is near an area where there is traffic wait for a time when there is the least amount of traffic since a cat may make a panic run directly into oncoming traffic.

Good luck and let us know how it goes. There's also alley cat allies website that offers wonderful information!