I have downloaded audio mp3 files on to a cd-rw but this doesn't work. How do I convert mp3 files so they will play on a cd player and what kind of cd media do I put them on?

First off. Many cd players can play MP3 but not all can. So the disk may still be good. Many dvd players also play MP3 so you might be able to test it with one of those.

You can still use a CDR for your recording. You just need an authoring program so it converts the MP3 to a reguler cd format.

One that comes to mind is Nero. But there are others out there for free. Try googling MP3 to cd and you should get a hefty list to choose from.

As mentioned, nero can burn audio cd's that will play in standard Cd players

Here is a free version to give a try if interested
BurnAware Free Overview