Reddit mentions of Tru Catch 30D Heavy Duty Humane Live Animal Trap

Okay, I have a big heavy-duty one https://smile.amazon.com/Tru-Catch-30D-Humane-Animal/dp/B00KHV1A5Q/ref=sr_1_3?ie=UTF8&qid=1498013449&sr=8-3&keywords=tru+catch+traps because I help with a lot of these. There are less expensive ones for sure.

There's also something called a drop trap that is a metal version of the box + stick trap in looney tunes cartoons. You place a little food under the box, prop up one end, watch for kitten, and pull the prop. I don't like these as much because I worry that it'll fall on a limb or tail and injure the animal. The humane traps like the one I linked has the bait way inside, and the door doesn't snap shut until the animal steps on a little shelf at the other end. It scares them with the snapping, but it's harmless. If you can find an experienced person to show you some tips, it'll be way easier. Stuff like, put newspaper down on the floor of the cage so the wire doesn't bother them walking in, cover the whole cage with an old sheet so they can't get the food out another way and aren't weirded out by the wire mesh, put the trap where and when they're used to being fed (if you know), don't feed for a day or two before laying the trap so they're highly motivated, and this trick for getting mama. Once you've caught the kittens, put them in a separate carrier or cage (you can use a carrier or get something called a transfer cage) and place it abutting the baited end of the big trap. Cover the whole thing with sheets. Mama will hear her babies and have to go into the trap to get to them.

Good luck! You're doing a great thing for all those cats and for your community.