www.wysiwygwebbuilder.com

How do I set up a media player (either audio or video) with user ability to select from a directory?

Maybe one of the following it not then please be more specific..
HTML5 audio with playlist
https://www.wysiwygwebbuilder.com/audioplaylist.html
HTML5 video with playlist
https://www.wysiwygwebbuilder.com/videoplaylist.html
jPlayer
https://www.wysiwygwebbuilder.com/jplayer.html

I need it to list the contents of an online directory of (for example) .mp3 files, and play the one selected. I had a flash player plug-in to do this which, of coarse, no longer works.

I assume since the files are in an online directory that these files change often? If not, then you should be able to use one of the extensions BaconFries suggested; otherwise, none of these will work as they don't read files from a directory.

I need it to list the contents of an online directory

Are the MP3 files stored on your own server? If so, use the built-in PHP File Listing extension.

How do I... (1) implement the php file listing extension and (2) how do I connect it to a media player?
Sorry to be so dense.

Sorry, there is currently no standard solution to load audio with playlist from a folder on the server.