How do I install a water line to my refrigerator?
They make "taps" specifically for that purpose - you can get them at home depot/lowes or probably any plumbing store.  

They clamp on to an existing water line and have a sharp pin inside.  You attach a vinyl or flexible copper line to it and run it through the floor to the fridge.  Then you crank handle on the valve down and the pin punctures the copper water line and lets water into the valve.  

When I did mine, I was a bit worried it would leak at first (they just look like something that wouldn't seal well) but haven't had any problems with it for well over a year now.