Removing vocals from songs is generally a fairly simple process, but results can vary widely from perfect to being a complete failure. (Vocal removal is sometimes referred to as "karaoke mode" or "center panned audio removal".) There are a few factors that affect how well the vocals can be removed. To understand those factors, it's best to know how vocal removal works first.
Vocal removal only works with stereo tracks, and will not work with mono recordings. This is because it works by subtracting what is common in the mix between the left and right channels. Since vocals are almost always panned in the dead center with equal amounts of the vocals in both the left and the right channels, they get removed very well, and in many cases, they are completely and perfectly removed. However, by removing all common elements from both stereo channels, other elements are also removed.
Typically bass is removed from the song along with the vocals because like vocals, bass is often mixed in dead center. The reason is that bass sound is non-directional for the human ear, i.e. You cannot tell what direction low frequencies originate from. Take any typical home theater system as an example. The home theater system will have six speakers: front left, front right, front center, rear left, rear right, and the low frequency effects (LFE) speaker (often called the subwoofer). Each speaker has specific placement requirements except for the LFE speaker, which can be placed anywhere convenient.
With the bass portion removed, bass guitars, kick drums and similar low frequency instruments are also removed. This isn't necessarily true for many orchestral recordings due to the way that they are miked.
If your goal is to remove only the vocals so that you have a karaoke version, you can add parts back into the mix with proper EQing or bandpass filters. To EQ the bass back into the mix, adjust the left EQ bands up by something like 6dB, and the right EQ bands down by 6dB. The only important thing is that you adjust them oppositely. It's not important to have the bands adjusted by the same amount, e.g. Setting the 80Hz left to +7dB and the 80Hz right to -4dB is perfectly fine.
Adding parts back into the karaoke mix like this works because it effectively changes the left and right channels in the affected frequency range to make them different. So when we eliminate the parts that are common to each, like the vocals, those frequency ranges that we changed no longer share the same information and it's left in.
This also works for the high frequency ranges where you will find the sound from instruments like high hats and snares. However, there is likely to be some vocal information there that could be added back into the karaoke mix, and moreso for female vocalists. A process of trial and error will generally yield good results.
As a rule of thumb, to add back in bass sections, set all the left channel EQ bands below about 200Hz to about +5dB and all the right channel EQ bands below about 200Hz to -5dB. This gives you an effective difference in the range of 10dB without adversely affecting the volume too much.
There are things that prevent vocal removal or limit its effectiveness to varying degrees. From above, it can be inferred that off-center vocals are not removed effectively, though this can be somewhat corrected for by "shifting the sound stage" (see Shifting the Sound Stage for more information).
Time-based audio effects often reduce vocal removal effectiveness. Examples of time-based FX are reverb, echo, delay, phaser, flanger, and chorus. Flangers aren't commonly used on vocal tracks, but reverb is extremely common. Some styles of music tend to use more of specific FX for specific instruments and vocals as well. e.g. Distortion is most often used with guitars, and almost always with used with heavy metal guitars, but not used on vocals. Reverb is more commonly used on vocals in dance and pop music than it is used on heavy metal vocals.
So if the song that you're trying to remove the vocals from has a lot of FX like reverb on it, you may not be able to reduce the vocals at all. C'est la vie! These cases happen, and there is nothing to be done about them. All you can do is work with the song the way it is, or move on to the next song.
Lossey audio compression can also reduce the effectiveness of vocal removal. MP3 is lossey audio compression format, and while it is very widespread, it isn't the ideal format to work with. To avoid this problem, when ripping music CDs to disk, use a lossless audio format like WMA lossless, FLAC, or WAV. By preserving all of the audio information, the vocal remover has better data to work with and can do a better job.
For information about removing instruments from songs, please refer to Filtering Instruments from Songs.
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