how do I hook up plastic pipe to copper pipe?
Go to hardware store and purchase the correct fitting for the job. There are different types and the choice is up to you. They make the kind you have solder to the copper or compresson fitting type. Same goes for the plastic side. You will have to know the size of both pipes you are fitting together. and the hardware store should have someone there that can help you figure it out, just ask, that's what they get paid for. By the way, if this is an older setup and you are placing something like a water filter onto a pipe (plastic filter connections and copper water pipe) you need to run a solid wire to connect the copper pipe back together just in case the electrical connections to your house is grounded by the water pipe. Good luck.
They sell couplers, PVC to copper at Home Depot or Lowes.
Solder a female threaded adapter on the copper pipe and use a male threaded adapter to switch to plastic pipe. Female plastic adapters have more of a tendency to split, thats why using a male adapter is better. If the area of the change is not in an always accessible place, do not use a compression fitting as this violates code.