Animal control?

Hey guys, so there’s some stray cats that go around my neighborhood mainly at night and they like to especially sleep under my family’s cars which are parked right next to my bedroom window and there’s two that usually get into fights with eachother which make it incredibly difficult for me to sleep since they’re sooo loud. They also like to go in my yard since it’s spacious and grassy and will poop there or sleep in it sometimes. Basically they’re annoying as hell. I just got a puppy too and when we take her out to the yard she’ll tend to chase the cat away but I don’t want her to end up running out to chase the cats so I really want to get animal control to get them. The problem is I’ve never used animal control and don’t know how they work... so I have to catch the cats and then they come pick it up or do they come catch them themselves? And do they charge a lot? If anyone knows about it please give me some details. TIA