Took black wire from switch, hooked to brass side of plug. Took white wire from switch and hooked to silver side of plug. Hooked ground to green screw of plug. I checked with meter, one pin to black, one to ground, light on. Also checked same with white, one pin to white, one to ground, light on. Tried this with two new plugs, neither work, why?

You have no neutral conductor, and not to be unkind but if you do not understand that basic feature of switches and electricity, you probably shouldn't be attempting electrical projects.
Please consult a licensed electrician.

That is a switch loop. You would never have a black and white on a through hot wire circuit, only black. You cannot get an outlet.

A switch is used to interrupt the "Hot" conductor only. There is no Neutral return used on a typical switch.

The white conductor is the feed to the switch and the black conductor is the return from the switch to feed the circuit.

What you have to do is follow the white conductor back to it's origin. It should be capped together with a black conductor.

At that connection point, there should also be a white (Neutral) conductor usually within the same cable. In order to get the receptacle to work, a new cable will have to be run from the origin of the supply cable. White will need t be terminated to the silver screw on the receptacle and the black would then be connected to the brass screw.