Good question. I went thru this research myself a few months back and learned a lot. You have several options in ascending order of expense. Its interesting because this question is the source of a lot of debate on this board.
1) As Maxz24 says just buy an RCA cable with 2 rca jacks on one end and the single headphone jack on the other end. Do this first. Its worth the $10 - $30 you'll spend just to try it.
2) Don't hook your Nano to your stereo. Buy an Ipod dock ranging in price from $100 - $600 and listen through the dock's speakers. I obsessed over several choices on up to the B&W Zeppelin and came to the conclusion none sounded good enough.
3) Buy an Apple TV (ATV) and use it as your house IPOD using higher definition lossless files. The Apple TV is essentially a video IPOD with a digital output so you can use an outboard DAC if you want better sound. It is $329 for the 160 gigabyte model and will allow you to control your music menu on your TV. Even with the RCA jack analog output, it will sound quite good and probably just as good as the source on your $350 stereo. It also gives you the ability to store and view your pictures, and video library on your TV via an HDMI output.
4) Buy the Wadia ITransport that is an IPOD dock that supports the Nano and gives you the capability to get digital output out of your IPOD to your stereo if you use an outboard DAC which converts the digital signal from the dock to an analog signal that will go into your Pioneer via the RCA audio input jacks. The Wadia is $379. You can use it without the DAC with just the RCA output similar to option 3. Its video capability is associated with passing the video through from the IPOD to a TV. Since your Nano does not have video, this is not applicable.
5) Improve on 3) or 4), by also buying an outboard DAC to get really good sound by using the digital out on your ATV or your Wadia and having the DAC convert it to Analog using higher quality DAC chipsets. $400 - $4000 and up. This gives you the capability to create a audiophile quality source from your IPOD and Dock or your ATV
The good thing about this list is you can work up the list over time if you prefer and as your wallet allows.
I did 1) and found it useless. Not enough power and sound into the stereo. Then I did 3) and thought it was not bad at all and really liked all the other cool features of the ATV. Then I did 6) because I read this board and some audiophile mags and I was bored on my Christmas break and my receiver and speakers are just good enough to notice the difference. Remember once you've done options 3&5 or options 4&5, you've created a really high quality SOURCE for a stereo - any stereo, so if you want to upgrade your amp/receiver and your speakers later you can still use the source you've created.