They can’t be caught hook and line (plankton eaters). Only netted or, if you’re feeling adventurous, try bow fishing and sticking them when they try to jump in your lap.
As a young kid we would go down to the creek and spear them - 2nd to 5th grade or so. Later would bow hunt them - even went on a few “hunts” in high school. Lots of fun chasing carp around!!!
The nearest trash can would take most of the carp. A couple were brought back to a neighbor for his compost pile. And a couple were placed on the doorsteps of various friends and enemies as either a practical joke or just to be mean.
The thought never crossed our minds to eat them. Although in Europe they are a huge sport fish. And I think you can fish for them using doughballs, corn, etc. on the bottom. Not so much plankton eaters - but bottom feeders - of most anything.