Someone help. How do you delete a contact on the new iPhone 5C!

So I got the new iPhone 5C today, and for some reason, both my facebook and iCloud just linked all my friends' contacts to my phone's contacts, and I have no idea how to delete them. I clicked edit on the person in the contacts, scrolled down to unlink and delete contact, and clicked "done" but when I went back, the contact was still there. HOW DO I DO THIS!

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