There are four common options for successfully connecting your MP3 player to your car stereo. I will list them here in optimal order from best to worst it terms of setup and quality.
1. Almost all newer car stereos come with a AUX in jack on the front of the stereo unit. An AUX in will be a hole on the face of the stereo that matches the size of the headphone jack for your MP3 player. You will need to connect your MP3 player to this AUX in hole with a stereo 1/8" cable. You can do a search for these on eBay and find them for less than $5. If you are a little more impatient, then you can find them at your local Radio Shack or Frys Electronics for not much more. Simply plug the cord out of your MP3 player and into the AUX in port on the car stereo system, select AUX as your input device (other options will be CD player, FM, AM, etc.), and then turn your MP3 player on. This option will not power your MP3 player, so either charge it up good or have a charge in your car that will adapt to the cigarette outlet. (Some very high end stereos can connect to Apple's iPod and allow you to browse your song library on the stereo instead of on the iPod.)
2. Another way to connect the iPod will be on semi older systems that have stereo AUX in RCA on the back of the unit. RCA is a connection that looks like the audio for connecting your TV sound and is usually signified by a cable with two ends, one white and one red. In order to successfully hook up your MP3 player to this scenario, you will need to invest in a stereo 1/8" to Male RCA cord at your local Radio Shack. Pull the stereo out of the console. Hook the white and red RCA ends with their corresponding female RCA ends on the back of the stereo and then wrap the cord out of another socket to the side of the console to the place you commonly keep your MP3 player. Plug the 1/8" inch side of the cord into your MP3 player, power it on, and there you have it.
3. One option for MP3 playback through your stereo is to use the FM airwaves. They sell FM transmitters at most mass merchant stores like Target & Wal-Mart, as well as online retailers. Decent FM transmitters run in the $20-35 range. The way these work is by plugging the supplied 1/8th cord into the headphone jack on the MP3 player. Then on the FM transmitter you can select a FM channel. Tune your stereo to the corresponding FM channel and you should be able to hear your MP3s through the airwaves. This option needs power for the transmitter to work. If you're lucky and have a couple of extra dollars, you can invest in a charger that powers both your MP3 player and FM transmitter. Some FM transmitters have battery options for power as well. This option is capable to have audio dropouts if you drive very far and radio stations change. It's best to choose a station that isn't being used for broadcast.
4. The last decent option for listening to your MP3s is to use a Tape Deck. They make a tape adapter with an 1/8" cord coming out of it that you plug into your MP3 player. Stick the tape in your stereo tape deck and the other end to your player and listen to your tunes flow. My only caution with this option is that a lot of these types of devices seem to get stuck in the tape deck rendering both devices useless. Consider yourself warned.
Good luck and enjoy the tunes!