A relay is like a switch with an electro magnet controlling its on and off. A wire goes from your car battery to one side of the switch. Your radio power wire goes to the other side. HOWEVER, the switch is held open. So your radio gets no power. You then take a wire that becomes hot when your ignition is on and hook it to the magnet wire. Then when you turn your ignition the magnet closes the switch and your radio turns on. Why would you do this? Because modern radios can draw to much power (current) for the old wiring. But you dont want to give up the radio turning on and off with the car. Thus you use the ignition to power the magnet to turn the radio on. In the pic bellow, the top battery would be your car battery. The bottom battery would be your ignition switch.
Sounds like to me you need some hands-on help. Kind of hard to walk you thru something like this on a keyboard.
The stereo will come with a detailed diagram designating the color coding for the stereo. Truthfully you can probably get it installed fairly cheap with the purchase of the stereo and speakers.