You can use Folders to organize your documents in whatever collections make sense to you. Documents can be in more than one folder. Look for the Create Folder button at the top of Mendeley Desktop or Mendeley Web.
You can assign tags to each document in your Library and use these tags to help to locate and organize documents.
You can also use the star icon to mark favorite documents, and mark documents as read or unread using the green circle.
This video (from 2011) provides a good overview of how to navigate and organize your Mendeley Library.
Where your database files are stored depends on your operating system. The default location for the different operating systems is:
When you add PDFs to Mendeley, it will create a link to where the PDF is stored on your computer. If you later move or delete the PDF, the link will break. It is important to move your PDFs to where you plan to store them before adding them to Mendeley.
Or, take advantage of Mendeley's File Organizer (in Mendeley Desktop: Tools - Options (PC); Preferences (Mac), which moves files from wherever they are imported to a designated Mendeley directory on your hard drive. You can choose to have the files automatically placed in subfolders (based on such characteristics as author name) and to automatically rename PDFs with a standard name structure. If you do not already have a good file organization system on your computer, this may be helpful!