Sorry to say, there is no perfect way of doing this. The link you provided uses the same technique I was going to describe but this requires that you have the original and an exact instrumental copy. Even that technique is not perfect and will still have some background noise.
One piece of AWESOME software that does this with techniques that are far beyond my understanding is Melodyne. You can actually isolate many parts of the song with this software. Only downside is the cost and, at least from what I've researched and been told, the isolation isn't perfect. My experience with this program is quite low since I just obtained it so there is more than likely a way to decrease the amount of background noise that comes when you isolate a sound. Melodyne is also great for fixing pitch in recorded vocals and is the reason I got it.
Of course the best way is to use the technique you already discovered or just asking the artist(s) for the isolated vocal track ^_^