I am wondering how you are able to take the words/singing out of a
song, so the music is the only thing that is left.

The technique usually relies on the fact that the vocalist is
positioned at the centre of a stereo sound stage and will therefore
appear equally on the left and right audio channels. Instruments which
are left-of-centre or right-of-centre will appear unequally on the two
channels. It's therefore a matter of subtracting sound that appears
equally on both channels, which has the effect of removing the
vocalist but leaving the instrumentals.

Descriptions of the technique are at:
http://www.vocalist.org.uk/eliminating.html
"Yes you can remove the lead vocal from a prerecorded song, but only
if the vocal is panned directly in the center of the stereo field. And
even then, the process isn't perfect. There isn't currently any audio
software on the market that can analyze and remove only a single vocal
part. Instead, you have to cut out the material in the middle of the
stereo field. That means cutting out the vocal and everything else
centered in the field."

Owain

Is there any free software that can do that?

This may be of interest to you:

http://www.g4techtv.com/callforhelp/features/40255/How_to_Remove_Vocals.html

Thank you both very much!