If you have never done it before, you might be better taking it to a stereo place or auto electrics and I would guess they'll charge a tenner for doing it. If there are no lights on the stereo when switched off, it shouldn't cause the battery any problems (unless obviously you accidently leave it on)
...or DIY version; remove stereo, normally done with metal strips down each side or removal pins depending on stereo and a firm pull, then behind you will see the black, yellow and red power supplies, along with all the speaker/RCA wires. In your case it sounds like yellow & red are connected together. This
may have been done because of a commen fault with your ignition switch (behind the barrel where your key goes) is damaged and you
might need to get this replaced. (approx. cost £20 + £20 labour) Hopefully not though.
(Its a dead easy job to re-wire stereo, with the hardest part can be just getting the stereo out)
If you need to re-wire, I have always used block connectors for easy/tidy connections like below.
