First, in order to do this, you need to find a radio edit of the song that you like, with vocals. Then, you also need to find the exact same version of the song but as an instrumental, ie. without the vocals. If you can't find both of these two versions, then this trick won't be possible.
Next, you need to import the two audio files into your sequencer. Line them up perfectly in parallel, down to the millisecond (actually, to the exact sample). You need to be able to play them simultaneously so that they sound exactly like just one song (except for the vocals standing out, of course).
Now, convert each track to mono, so the two stereo channels are combined in each track. They need to be panned to the center.
Once you've done the above steps, and you know that they are completely synchronized, then take the instrumental track and invert the phase of the entire track.
Now, play the two tracks together, or bounce them to disk. The phase inverted version in the instrumental will cancel out the waveforms of the music in the vocal version, leaving only the vocals behind.
Now if you cannot find the full song as both a vocal take and an instrumental with the same arrangement, then you're almost out of luck. The only rare exception is that if you have just the vocal version, sometimes (in theory) you can pull tiny snippets of the vocals out from the track by cutting it up and following the steps above (for instance if there is a chorus with vocals and another "chorus" chord arrangement in the song without singing). This wouldn't work with rock songs, because they are recorded live and they won't be exactly the same, even if the musicians tried to play them exactly the same. But in today's studio-heavy world, some pop songs which are computer produced are probably generic enough to make it work. I've never actually tried this, but in theory, you might find some songs that you could do it with.
Let's step back for a while and ask why you're separating the vocals from a song. I presume that you're trying to remix a track that you like. Are you doing it because you like that track specifically, and no other? If you're doing this as a project for an artist, they should be able to provide the vocals for you. If you're doing it for yourself, then you face a bigger challenge.
An audio file that contains only vocals and no instruments at all is called an acappella. This term is actually a contraction of two Latin words, "a cappella," which literally means "from the chapel," or figuratively, "from the choir." You can do internet searches for acappella tracks in all kinds of places: Google, torrent sites, and legitimate music sites. The trick is to remember that many people spell the word incorrectly. To search effectively, you should search for "accappella" and "acappella" and "acapella" (this last one is the most common spelling and yields the best results in searches, although some people argue that the one with two P's is more correct). If I had a preference, I'd like to see things spelled correctly. So if you're a producer who is releasing acappellas, let's see if we can change the world together, and start spelling it with two P's.
Personally, rather than bang my head against a wall trying to find vocals for a specific track that I want to remix, I do it this way: I'll spend half an hour on the net, trying to locate an acappella for that particular song. If I can't find one in that amount of time, I'm probably not ever going to find one. Sometimes, it is better to just admit defeat and look instead for acappellas in general, and then pick one that you like which is already available.
There are a lot of acappellas out there. If you search download or torrent sites, you can find lots of legal ones that you can download very quickly. Some have to be purchased, but many are free, depending on which sources you use. Go to www.beatport.com as an example. Enter "acappella" into the search engine, and you'll find several hundred tracks to choose from. Enter "acapella" and you'll find thousands.
In rare cases, if you are looking for a specific song, you can actually contact the artist and ask if you can have a copy of the vocals. Some artists will give these out, although it's pretty rare on major labels unless you happen to be a very well-known remixer with a lot of previous credits on your resume. Many smart studios/artists will recognize the fact that the more often that their songs are remixed, the more publicity (and therefore royalties) that go to the copyright holders for the songs. The remixer doesn't get any royalties (except in certain uncommon exceptions for top remixers). Usually, all the money is made by the original artist (or I should say, more accurately, by the studio). Of course, you do also have to recognize that a bad remix of a track doesn't help much, because it won't get played and therefore won't drive radio-play or other royalties. Some artists/studios will provide vocals under strict conditions that the artist/studio gets to review the remix first before it is allowed to be released, and they have the right to prevent the remixer from releasing the remix if they don't like his/her version of the song.
So anyway, the moral of the story is that if you have your heart set on remixing one specific song, sometimes there are options. But usually, I find it is best to listen to some of the thousands of vocal recordings that are already out there, and choose one of those readily-available tracks to remix.
Good luck with your remixing projects!
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