buy a 12 volt converter and plug your playstation into it
take apart your playstation and follow the 110 volt cord that goes into your playstion onto a small circuit board and remove the circuit board but not after you note which wires are positive and negative that are coming OUT of that small circuit board. That circuit board is a 12 volt converter. You don't need it because your car is 12 volts. Just hook up +- from your cigerette lighter or radio wires (whatever is controled by your ignition) to your playstion wires and presto you have power.
the audio can be done a few ways
fm modulated which is achieved by intercepting your antenna connection through a modulator box and connects to the audio to your playstation
or
If you have a radio with audio input like on high end aftermarket decks you can directly connect the audio wire to your deck.
If you have a pioneer aftermarket deck pioneer sells a cdrb10 for about 35 dollars and utilizes the cd changer controls to become audio inputs
if you have a stock stereo fm modulated is the only way to go
have fun