When you enter the media library you'll see two sections. On the left side is a list of all the uploaded media. This list contains attachments that are added via the library itself and attachments that are added via the message composer. You can add a title, a description, and tags to the attachments as well.
Uploading media within the media library is done on the right side of the media library. Click on 'Media File' or 'Link' and add the attachment. When you add a media file you can browse your computer for the file. Once you've chosen the file, a process bar will appear, but your attachment isn't uploading yet!! You can still add additional information. If you don't want to add additional information you can just click 'Upload' in the bottom right corner.