How does one get a start in copyediting and what are the credentials needed?

I'd suggest you look into taking a copyediting course so you have a qualification to back you up and to give you knowledge of copyediting symbols. Have a look at the Publishing Training Company (see link). You need an excellent knowledge of spelling and grammar.

Sometimes it is advisable to begin in proofreading and work your way up to copyediting. Also, it's not a case of getting a qualification and walking in the door. I would suggest trying to gain as much experience as you can. Get in touch with charities, local organisations that publish newsletters, free newspapers etc, put an ad out and offer to copy edit disserations and build up a portfolio. Network, tell everyone what career you're trying to get into and try and make contacts.

Also, I know you haven't asked this and it may seem a bit obvious but copyediting is a different career to being a writer so make sure you know this is what you want to do and don't assume you will enjoy it because you enjoy writing. If you get a job in copyediting then you work in editing, don't assume that working in editing allows you to transfer into writing articles if that's what you're interested in. Sorry, you may already know this but I think it's worthwhile to point this out just in case.

EDIT

Oh I also meant to say this field is very competitive. It would help if you had a specialist area i.e. law, science, engineering, medicine. People with knowledge of the specialist vocabulary required are wanted for such positions, it's more difficult to find a job copyediting bestselling novels for example.