Do I give my copyright away when publishing open access?

What happens to the copyright depends on the arrangements that you make with the publisher. When you submit an article to a traditional, you typically give away the copyright to the publisher by signing the 'copyright transfer agreement'. When you publish in open access journals you typically retain the copyright. Open access articles usually have a Creative Commons license, which means that you retain the copyright and by way of license indicate what others are allowed to do with the article.

Also see: What are Creative Commons licenses?