"I can't import mp3 files into iTunes 11" you say. I hear your pain.
Disclaimer, I am not importing music from audio CDs. If you're looking to do that look at the apple documentation here.
Attempts
There are various ways of 'importing' an audio file into iTunes. You can drag and drop it into the window (you even get a little green plus), you can 'open with iTunes', and you can iTunes-> File-> Import Media. If none of these worked for you, you're not alone.
You might have thought to change various import settings. Nope! Those won't help you. They are geared towards importing CDs.
If you see a thread on Apple support telling you to download and compile some program to check the mp3 for 'encoding errors', ignore it.
Solution
You need to change the file format of the mp3. iTunes doesn't like to work with mp3s, it much prefers .m4a files. Don't Panic! Before you run out to purchase some sort of audio conversion software remember, you have Quicktime. Luckily Quicktime can convert your file and send it straight to iTunes.
How to send your mp3 to iTunes
- Open your mp3 in Quicktime (make sure it plays)
- Quicktime Player -> File -> Export -> iTunes...
- Wait for it to complete.
- Check your iTunes library for the new file. I'd check the 'Recently added' smart playlist.
Hopefully this works for you :)
But Wait a Minute...
Why was this so hard? Why did iTunes fail silently whenever we tried to import an mp3 file? Is it too difficult to tell the user what is the matter? Furthermore, Apple definitely knows how to convert this kind of file. Why wasn't that an option?
I think the answer is one of business. Apple wants you to buy your music from the iTunes store. If you already have audio CDs you are allowed to migrate to iTunes, but music from other digital music retailers is discouraged. After all, importing a CD is handled very gracefully by iTunes, therefore any other digital media must have been obtained through competitors.
Failing silently is very poor taste.