How can I power a vanity light from a ceiling light switch circuit?
The best way is to identify lights that you want switched together with the new lights, and run a /2 cable from those lights to the new lights. 

The new lights' black and white go to black and white on the cable.  

In the old box, you look at where the black and white from the lamp itself go to.  The black and white from the new cable go to those same places.