How can I transfer an MP3 voice recording onto my computer from my Nokia Lumia 920? The file doesn't show up in my phone.
Go to the app that you used to record the MP3. There should be an option to either save the MP3 to your music library, or to upload it somewhere (usually OneDrive or DropBox). There might also be an option to "Share" the file, which would let you send it as an email attachment to yourself or send it to a computer via Bluetooth.
If you save the file to your music library, it should then appear in your Music folder when you browse the phone's storage via USB. It will probably be under "Unknown Artist" or something like that; just search around a bit and you should find it. Some apps also create a separate folder under the Music library where your recording will be saved. The app may let you specify the artist and file name before, or when, you save it. You can copy it from the phone's music library to your PC using USB (use Windows Explorer if on Windows, or any other program that supports MTP, the Media Transfer Protocol).
If you can upload the file to "the cloud", then you can download the file from that same service on your PC. OneDrive is probably easiest, since you'll already have an account (the Microsoft account you use with the phone gives you a bunch of free OneDrive storage).