First of all lets talk about the head unit. The head unit in a car is the actual radio and CD player in the car located in your dash. This powers all of your speakers and is a main part to change when considering to upgrade your car audio. The stock head unit in most cars do not have many features or a lot of power capable of providing good quality sound. When looking for a new head unit you must determine whether it is a single din or a double din. Single din head units are half as tall as a double din head unit, that is how you usually determine this. Once you have figured out the size din you can go shopping for a new head unit. A new head unit might offer great new options such as a DVD player with built in screen, availability for a mp3 player input, satellite radio input. Some also have Bluetooth capability and HD radio. The more features the higher the price is going to be. And with all products sticking with a name brand is usually a good idea.
Now that you have a head unit picked out you need to find some good speakers that will go along with it. This step is not necessary, you can still get good sound out of your stock speakers sometimes by just changing the head unit alone, but it will sound much better to get new speakers as well to compliment the new head unit. You can either decide to buy speakers based on your head unit or based on an amplifier you can add to your set up. If you base your speakers on your head unit check the head unit's specifications. If the head unit says (50w RMS x 4ch) this means the head unit can power a minimum of one speaker per channel and with the proper wattage of 50 RMS. So to find a speaker you must choose one that has a RMS wattage rating of a little under 50 (its a little less so that we make sure the speaker can be completely powered for better sound)and a max wattage of at least double the RMS wattage or if it is listed on your head unit a little more max wattage than what is listed (this is to prevent your speaker from blowing out). The RMS wattage is the amount of power the speaker can handle while still maintaining good clarity. Max wattage is the total power a speaker can handle before it starts to overheat and fail or blow out. You can add more speakers per channel, but most people stick to one speaker per channel. If you are using an amplifier with your set up instead of basing your speakers on the head unit you base them on the amplifier. The amplifier ends up over riding your head unit and you just use the specifications that are listed on the amp to choose speakers, using the same RMS and max wattage information talked about above. A general rule that is good to remember is that Max wattage is usually twice as much as the RMS wattage rating, and that is if you had to guess because it is not listed anywhere.
Speakers come in many shapes and sizes make sure they will work with your car, the best bet is to match the size of the existing speakers or you will have to do some custom work to get new ones ti fit. Speakers can be one way, and go up from there to three way and four way. What this means is it breaks the speaker up into sections. It breaks it up into a woofer, mid woofer, and a tweeter (more if its more than three way). The tweeter then handles all of the high level audio, the mid woofer handles all of the middle tones, and the woofer handles most of the low tones or bass. Three way speakers or higher can sound extremely well because of the way it breaks up the sound, but it is all based on price and preference.
You can also add a separate sub-woofer to your system to get some more deep bass. You can add this to your amplifier there should be an option on the amp, or some head units may offer this option. Sub-woofer enclosures can be custom built to fit your car, they can be purchased already made or you can replace your rear speakers with sub-woofers if you like.
If you follow this helpful guide you should be able to choose the right set up for your car. But i still advise you to seek some help if you are unsure about anything, you don't want to mess up anything in your car.