I can't work out how to publish a draft. I go to preview, to check everything's ok, and then there doesn't seem to be any option to do anything more.
The preview usually opens in a new tab/window for convenience. Even before going to preview, there should be a blue 'Publish' button present in the same area as the 'Preview' button, "the same area" being the Publish metabox.
Below is what the Publish metabox looks like in the latest version of Wordpress (3.5.1).