Besides the general effects on the nervous system, there are a few specific effects of alcohol which make driving dangerous.
Vision. Since alcohol is a depressant, it affects the way nerves transmit impulses. The muscles relax and some control over them is lost. The human eye is not impervious to this effect. In normal situations, light enters through the pupil, and is focused by the lens onto the retina, where photoreceptors are stimulated by the light, and interface with two kinds of nerves which transmit the picture out of the eye. Alcohol interferes with the muscles which enable us to see images properly.
One group of muscles, the ciliary muscles, is used to flatten out and release the lens, which in conjunction with the non-adjustable cornea, is responsible for properly focusing images. Under the influence of alcohol, the ciliary muscles are relaxed, and the drinker's vision becomes blurry and unfocused.
The pupil of your eye is like a camera's shutter. It contracts and expands to let in the right amount of light for a good image. In bright light, it decreases its diameter and lets in less light. In dim light it increases its diameter to collect more light. When driving at night and you see headlight glare from passing cars, your pupil contracts in one second to prevent being dazzled, and opens up after the car has passed. Normally you regain your night vision after seven seconds. However, under the influence of alcohol, these times are increased. When a drunk driver is passed by headlights, his eyes cannot adjust as well and he drives semi-blind for several seconds.
Three pairs of muscles in the eye are used to enable the eyeball to rotate in any direction. These muscles work closely together to ensure that both eyes are pointed in the proper direction to focus on an object. However, when alcohol is present, these muscles cannot work together properly. The result is double vision. The driver sees two cars coming towards him. Which does he steer away from? Also, the proper spacing of the images between the two eyes enables the brain to estimate distances. This is known as depth perception. When the two eyes are not working in tandem, depth perception is altered. Changing lanes, passing another car, and many other driving tasks are heavily dependent on distance judging.
When you drive, not only do you see what is directly in front of the care, but you (hopefully) also notice things around you and to the sides. Buildings, houses, street signs, and cars in other lanes. Things in the corner of your eye. Even if you do not see these clearly, you know they are there. This is known as peripheral vision. Alcohol affects the peripheral vision. A drunk driver will not notice a person walking out onto the road, or a car turning into the road from another street. Seeing potential dangers like these is crucial to safe driving, and a drunk driver cannot see these things.
When alcohol affects the way your eyes work, all you can see is the blurry, double image directly in front of you. This is extremely dangerous for driving.
Concentration. Driving is a very complicated task. It requires the driver to pay close attention to many different things, and make adjustments, all at once. This is called a divided attention task. Alcohol seriously affects performance on divided attention tasks. It impairs the rate at which your brain can process information, thus making it difficult for the brain to manage the divided tasks properly. An unexpected situation requires a quick divided attention judgement and reaction. Under the influence of alcohol, this is impossible. A drunk driver is not able to react to an unexpected situation properly. While a drunk driver might be able to do one or two well-practised tasks such as driving a straight road, or a road they know very well, an unexpected turn or car can mean disaster. Also, driving with friends in the car or the stereo on can be distracting, but more so to a drunk driver, whose attention doesn't necessarily stay on driving.
Observation skills. The slowdown in mental processes also affects all of the individual tasks needed to drive properly. It affects how you observe the situation around you, including keeping watch for other cars, road markings, signs, turns, traffic lights, pedestrians, cyclists, parked vehicles, etcetera. Observation skills include not only looking in front of you for these things, but periodically checking mirrors and blind spots. Maintaining a close watch on the situation around you is absolutely vital to driving. Alcohol can interfere with this activity.
Tracking skills. When you follow the curves of the road with your steering wheel, your brain is doing a function called tracking. You are coordinating the movements of your hands with the image of the road that you are recieving. To keep in your own lane or to make a turn requires skilled tracking, and alcohol can affect this. Typically the drunk driver makes periodic gross corrections in direction rather than keeping a smooth, constant tracking task going.
Reaction Time. When you notice a dangerous situation, you often have to make a quick reaction to avoid an accident. Alcohol lengthens the reaction time of a driver, thus making any potentially dangerous situation much more so.
Hopefully, you now have a better understanding of just how complicated driving is, and how it requires carefully coordinated efforts from many parts of your body. Excessive alcohol makes it extremely difficult to perform this coordinated effort. That is why drinking and driving is unsafe, and why it is illegal. It is also important to note that all of these apply especially for inexperienced drivers. A driver who has not honed all of the driving tasks and made the entire process second nature is already dangerous to him/herself and to others; even a little alcohol increases this risk.