'99 Chrysler LHS
 

How do I correctly bypass factory amp and install my own amp and sub

if your wanting to use your own stuff like speakers then you run new wires to the radio or you get a wire diagram unplug the amp and make a jumper wire set or find one that will pass through the wires of the amp mainly the speaker wires.

I'm about to install subs and amplifier to my 97 LHS with the Infinity system. One difference you and I may have is that I am using an aftermarket radio with RCA outputs. The speaker level outputs are wired through the stock factory harness and I'm using the factory amp to power the stock speakers. I plan on running a set of RCA cables from the line out on the back of the radio to the rear of the car and the amp powering my subs.
One recommendation I have if you're using the factory radio is to just disconnect the wires from the rear speakers and run them to the speaker-level inputs on your sub's amplifier. True, this will disable your rear speakers, but bass is omnidirectional and only the passengers in the rear seats would lose definition. Front passengers would retain spacial imaging from the front speakers.