First, if you like I can do this for you and email the file to you. I would need the address of the Youtube song.
If you would rather do this yourself, the following is one method you can use to record the audio.
There is a program available for free download called "Wavepad".
Download siteTo save your song this way, you will need to have a microphone connected to your computer. You may have a video camera connected and these often include a built in microphone.
If you don't have a microphone or camera with a microphone you could use a recorder with an audio out jack. Then connect it to your computer and select audio in as the sound source in Wavepad.
When you install Wavepad you will need to select one other program from the software maker that is "shareware" meaning you can try it free for x number of days or uses, then to keep it you must buy it.
The Wavepad is yours to keep regardless whether or not you purchase the second program.
This program can record audio. I think the easiest way would be to start the recorder going, then open your YouTube song and play it.
Once the song completes, you can go back and stop the recorder.
Edit out the dead space at the beginning and end of the recording and save the file result.
You can choose what file type you prefer to save it in, including .mp3. The clearest sound will be .wav, though the file will be quite large in this format.
The Wavepad is pretty easy to use, but I would imagine that it will take some time and experimentation to get the results that you're looking for.
I hope this helps!
Dwight