I have been using Calibre to format my e-books, and I have been very happy with it. However, as PseudoCubic noted, it will not accept a Word document as input. Ideally, you should convert your file to html first and then format it with Calibre. If you convert your Word document to html, make sure you choose the Web Page, Filtered option. Otherwise, Microsoft adds a lot of extra tags and stuff that will really mess up your html file.
For some other suggestions on converting your file to html, I would recommend going to this guide by Guido Henkel. He will walk you through all the details for making sure that your html file is properly formatted first, and then he shows you how to use Calibre to include your cover image, table of contents, and other material.
I haven't used Scrivener, so I don't know whether or not it can create both file versions (ePub and mobi) straight from your completed document. If your book is already finished and you want to use Scrivener, then you will have to import it there first, and you may want to review your content to make sure the formatting still appears the way you wanted it. If you are a Windows user, you'll need to use the beta version for Windows.
There are other tools that will convert your files, but all of them work better converting html documents because the tags for the formatting are clearly defined. If you are comfortable working with html, then you may want to give that a try first.