Copyediting and copywriting are both very different jobs. A lot of copywriters breaking into the business might write for free initially to get their name out there, otherwise, they usually charge by the word, which usually depends on the length of the project. I'm a certified copyeditor and I usually charge around $50 an hour, depending on the length of the project and the level of editing needed. Proofreading is a level or two down from copyediting though and usually is cheaper.
What determines the price for writers and editors is education and experience. A certified copyeditor with experience is going to make more than a non-certified copyeditor with little experience, and an award-winning writer is going to make more than someone just breaking into the business. Like anything, you have to start at a lower price until you can build up your portfolio.