When you get message that has files or links attached to it you'll find them underneath the video player area (see the image to the right). If the attached item is a file, such a Word or Excel document, you can download it by clicking on its download link. You'll likely be asked to specify a location where to save the file.
If the attached item is a web link you can press the open in a new window. This will cause your web browser to open a new window and take you to the selected web page.