How Exactly Does Resistance Penetration Work???

I'm confused as to whether penetration is a simple subtraction or a division.
Say you cast a spell with 50% lightning pen against a mob with 50% lightning resistance.

Does the penetration then reduce the resistance to 0% or divide it by half and leave 25% remaining?

Also, if you have two sources of lightning pen, do they simply add together?

Answer to your question, and a little bit more:
http://pathofexile.gamepedia.com/Penetration#Examples

Resistances are already relative by nature, so their modifiers are usually handled additively.
So, as long as you see something in the form "+x%" or "-x%", you never have to multiply or divide anything to know the outcome (resistances, max resistances, penetration).
In your example, the penetration would reduce the target resistance to 0% (full damage).
Multiple sources of penetration would add together, yes.