Many options are available to those interested in playing their iPod Shuffle through their car stereo, but perhaps the cheapest, easiest method is connecting the device to the auxiliary output jack. Such jacks have become increasingly common in stock car stereos with the proliferation of portable MP3 players and can be found in many aftermarket car stereos as well.
Obtain a 3.5mm audio cable. Both general and electronics-specific retailers commonly carry them. The cable will have what looks like a headphone jack on both ends. Connect one end of the cable to the iPod Shuffle's headphone port. Across all three generations of the iPod Shuffle, this can be found on the top of unit.
Connect the other to the car stereo's auxiliary output. These are most often prominently displayed on the face of a car stereo and labelled as "Aux." Power on the vehicle. If the car stereo does not start automatically, turn it on by pushing in the volume knob or by the dedicated power button, depending upon the make of the stereo.
Switch the car stereo to the auxiliary channel. Most car stereos feature a "band" or "channel" option that allows you to cycle through AM, FM, CD player or auxiliary functions. Cycle through them until you hear music being played from your iPod Shuffle.
If your car stereo lacks an auxiliary jack but has a lighter/power port, devices such as the iTrip or Belkin Tunecast allow you to broadcast a weak FM signal that can be picked up by your car stereo.