with no idea what platform you are using, it's hard to help.

Search your hard drive for the name of a song to see what folder you set for completed downloads.

Only shared files show in the library, so I guess you chose not to share your download folder (which can be a good thing, especially if you inspect the files before sharing them back. That helps clean out some of the junk--or worse--that people inadvertently share). If you want to see your download folder in the Library, the Library File Menu has a command to "Add Folder to Share."

btw--some of the other posts already have a similar answer (reading them can avoid waiting around for one).

cheers