Permit me to giggle a bit here, but someone asked me how to do this about 30 minutes ago.
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Program: Audacity
If you want the music to be an MP3 once you've cut it, you'll need the Lame_Encoder.
Both are here:
http://audacity.sourceforge.net/download/windows
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To cut the music:
When you install Audacity, you'll need to open it, then close it, then open it again - I don't know why.
1. First of all, you'll need to know, to the second, where you want to cut from and to.
2. Import the music into the program (simple File > Open)
3. Zoom into the blue bit, until you can see the individual settings.
4. Drag and highlight (as you would do in Word) the bit you want to cut with the cursor.
5. Cut it (it's worth going into Edit > Cut as Ctrl + X sometimes doesn't work)
6. File > New and paste the music into the new document.
To export as an MP3:
1. First download the Lame_Encoder (see above link)
2. Extract all the files into a folder (an empty one, preferably)
3. In Audacity go to File > Export as MP3
4. You'll get a screen telling you you need to find the "lame_enc.dll"
5. Click OK and browse to the folder you extracted the files to earlier
6. Select the "lame_enc.dll" (should be the only file shown)
7. Export
8. The files, unless you specify a different destination, export as MP3's into the folder with all the Lame_Encoder things.
If you need more help, then hit me up on AIM.
The picture attached is just basic things.
EDIT: If you just want to cut things in the music, delete what you've highlighted.
If you want to make cuts in the music - ie space - then I think you can drag what you've selected along a bit.