To connect your iPhone, iPad or iPod to your home stereo you just need a dock and a 3.5mm to RCA cable like this cable above. The RCA cable plugs into the rear of your stereo and the 3.5mm plugs into your iPhone dock jack.
This is an Apple iPod dock. It has a ‘line out’ output. (The jack on the left in the above picture).
The ‘line out’ will match the exact voltage and impedance of the ‘line in’ on your stereo. It doesn’t matter what volume the iPod is set to.
You can leave the audio lead and charger cable plugged into the dock permanently. It will also allow you to control your iPod via any Apple remote control.
When plugging into the back of the Stereo Amplifier, the normal input to use would be the AUX-IN, but you can use almost whatever input you want: CD-INPUT, TAPE-IN, TV-IN, DVD-IN or the AUX-IN, but do not use the PHONO-IN as it is designed specifically for a record player and won’t sound as good.
As for what cable to buy, they start as cheaply as 1c (e.g. here) but I’d steer away from one like that which uses cheap cable. Pretty much anyone can tell the difference in the sound on one of these cheap cables even if you don’t know much about music at all. But the difference between a mid-range cable and a high end cable is less noticeable unless you have a good ear and a good stereo. I use one like this which costs about $25, but you can buy one somewhere in the middle range for around $10 like this or this.
If you are buying a new stereo, Pioneer and others are now including AIRPLAY into some of their amplifiers. The amplifiers have a Wi-Fi receiver built in which means you can play from your iOS device over your Wi-Fi (Airport) network directly to your Stereo with no loss of quality. You don’t need to connect any cables.
If you don’t have a dock, you can plug the 3.5mm straight into your iPod headphone jack, but there will be a slight loss of quality. (You can read about why here.) If you do this, the best results set your iPhone volume to about half. If it’s too quiet you may get noise and hiss. If it’s too loud you may get some distortion.