I ran power to the switch, and made the correct connections at the first light, and its bright. However the 2d and third light are dim. Please help.

My first guess is that you wired the second and third lights in series instead of parallel. (The images are for DC circuits, but the concept is the same.

What happens is that the first light gets 120 volts, but the second and third lights only get 60 volts apiece--and therefore are dim.

Double-check your wiring on the lights. White wires go together, black wires go together. In the switch box, the white wires do not even go through the switch at all--they are just tied together. The hot black wire and the black wire from the first light will each go to one (different) screw on the switch.

I hope this clears it up.
WallyH