How do I transfer all audio files from a computer to an external hard drive?

You could use xcopy (from a command prompt) to copy all the files of the type you want (mp3?), on the entire hard drive, to the external drive.

I am assuming Windows. Open the Windows Explorer. You can use the W/E shortcut by holding down the Windows key and hitting the E. Once there, hit Ctrl/F for Find. Have it search for all music and video files. Once it is done, select all files and copy and paste.

If you don't care about organization (how did I guess that? ;-) you can perform a file search of "*.mp3" (substitute as appropriate for whatever format you typically use) from the root of your main drive. It will take some time, especially if your hard drive is on the large side. When the search is done, you'll have a giant list of files. Select all, cut, and then paste to your external hard drive (not the root directory, please). Be cautioned that various operating systems have limits on the number of files per directory and so on. P.S. Kurt's answer is equivalent, and he wasn't the slightest bit condescending, so I won't be upset if you choose his answer as best. ;-D