Add new light and switch from existing lighting circuit
Yes, you want to tap off the existing switch. 

First, get a 5-pack of colored electrical tape ($4 at the big-box).  Go into the existing switch box, make sure the black wires are switched and not the white (if not fix it).  Find the cable to the existing switch; the black wire will be switched-hot.  Mark it with red electrical tape.   Now, everything in the box is color-coded by function.  

Now, bring the black-white /2 supply cable to the other switch-light into the switch box.  Match up similar colors. And yer done! 

If you need to bring 3 wires together, use a wire-nut.  If you need to tie a second wire to a wire that's already going to a switch, use a pigtail with a wire-nut.  Alternately you can upgrade to more deluxe  $3-range switches which have a feature called "Screw-and-clamp"; these switch screws can take 2 wires each.