Audacity is a great piece of free software for audio recording and editing, but unfortunately creating an MP3 file from a recording isn't entirely straight-forward and regularly perplexes some of the Open University's Languages students (who have to record themselves speaking their target language and upload the audio file to the online assessment submission system). The fact that questions about this keep coming to me suggests that not all OU staff are entirely clear about it either...
There are two complications.
(1) The "encoder" which Audacity needs to produce an MP3 file isn't built in. (Apparently US patent law says that the Audacity people aren't allowed to build it into the software, but they ARE allowed to point us to another website where we can download it and build it in ourselves. This is one of those cases where the law is an ass and makes additional work for the rest of us. D'oh!)
Assuming you've already downloaded and installed Audacity (from http://audacity.sourceforge.net/), you also need to follow the link to the "LAME MP3 encoder" and install that too. When you first try to export a recording as an MP3 file (see below), Audacity will ask you to find a file called "lame_enc.dll"; hopefully it will be in somewhere obvious like C:\Program Files\Lame for Audacity, and once you've pointed Audacity towards it you won't have to do it again.
(2) The second complication is (apparently) simpler, and therefore (paradoxically) more difficult: the difficulty isn't obvious so the solution is harder to remember. To create an MP3 file from your recording you DON'T select "Save As" (or its nearest equivalent, "Save Project As") from the file menu, as you would if you were saving a Word file in a different format (such as .RTF or .DOC instead of .DOCX). You don't want to do that, because that would save your recording as an Audacity project, which won't be readable by anything other than Audacity.
What you need to do is to select "Export..." from the file menu; then under "Save as type..." select "MP3 files".
Easy when you know how. (But harder to remember.)
(For Open University staff: you can see the Department of Languages' guidance on installing and using Audacity on the website for any Modern Languages module, amongst the resources for assessment.)