In connections between copper and black plastic water pipe what is the proper connector?
Sounds like you are running underground piping, if this is the case you must use either L or K copper, which ever one is approved by the code official, polybuteylene pipe, the black plastic is approved in most places. The connector you would need for this application is called a Mc Donald coupler, or some places call it a Mac Pac and its available at most plumbing supplies. If you're working drainage piping use the appropriate Mission Bandseal also available at the plumbing supply.
J whatever has the right idea. But you dont always need a union. threaded adapters, compression, and special made adapters (copper sweat with a cpvc glue in coupling) are commonly used. But you may also have Pex tubing if it is black. If thats the case there are copper sweat/ pex crimp adapters. You could also use compression fittings. If the links J dude gave you dont look like what you have you may very well have pex. Years ago Pex was put under the slabs and crimped onto copper manifolds that are sweat togeather and stubbed out to the fixtures.
they actually make a union that is plastic on one side and copper on the other. You didn't mention whether you have pvc or cpvc (two different types of plastic pipe) But what you are looking for is either a cpvc copper adapter or a pvc copper adapter. cpvc is a yellowish plastic pipe, and pvc is white. It usually says what type of pipe it is on the side of the pipe itself. pictures of both linked below