You can buy an FM transmitter, especially designed to hold/connect/recharge an iPod, and your songs on the iPod will play through the FM portion of your existing radio unit. To work you must synchronize the radio and the transmitter to the same frequency, say 88.1 FM. Simple as that.
By the way , you can buy these units for $20 to $40- Belkin is a good brand.
G'Luck.