Do I need to run any wires to my after market stereo from my car battery?

No you don't. If you bough a wiring harness like you should have/should do then all the colored wiring from the new radio's wiring harness will match right up with the colors on the vehicle specific wiring harness that the plug you disconnect from your radio. it will have power/ground/turn on and all your speaker wires. BUT sometimes some vehicles have factory amps, and some chevrolet use a different way of turning on the factory radio so you have to run a wire from the fuse box and tap an accessory fuse that turn's on/of with the key for the turn on wire on the radio. If your having troubles stop by a local audio store and pick their brains on what to do for your specific vehicle.

EDIT: It doesn't take a genius to figure out that if you have a factory radio it has to be getting power and ground from somewhere so the wires ARE there lol. trust me, don't cut or hack the factory radio plug off, it will become a mess and it's easier just to buy the $15 wiring harness for your vehicle where there is no guess work and your not sitting there with a test light and a 9v battery trying to figure out which wire is which lol. trust me ive had to fix that kind of stuff many times before where people try putting in their own equipment and don't have a clue what to do when they cut the wires off.

u can use the wires already in the dash from last stereo. if those wires dont exist u got to run ur own

ok the yellow is frequently the consistent ability distant is in many circumstances a blue cord on aftermarket stereos and the black is the floor try applying a try mild with the main important off floor the testlight and touch the different end to the yellow if the sunshine activates then thats the consistent ability

Its more safer to run it to the cars own radio harness,if your replacing the stock radio purchase the harness,its easy to plug it right in.