Completely trashing a car is a difficult process, and very hard to do right. The goal is NOT to make your vehicle an undriveable wreck, but to give your vehicle character in a sea of bland automobiles. Done right, your favorite car will have plenty of distinguishing characteristics, be fun to drive, and the envy of all your friends. This process takes patience, determination, and last but not least, money.
The first decision you will make is which car? Try and find an old one, preferably with a good engine, a bad paint job, and at least a tape deck. A big engine will help you accelerate faster, and give you more power, but is not really necessary. The bad paint job is so you won't be worried about scratching the paint, because it will be scratched. And the tape deck is so you have something to do while you're having fun. Next, are you going to want an automatic, or a clutch? I prefer a clutch, it gives you more control over the speed of your car, slightly better handling, but there really isn't that much of a difference.
The next decision might take a bit of research. You'll need a nice secluded place, preferably paved, with plenty of curbs, potholes, and other miscellaneous stationary objects. You don't want to be worried about distractions, such as traffic, pedestrians, dogs, etc... Parking lots late at night, parking lots of abandoned buildings, and old unused highways all make good places to have some fun. If you can't afford the time, you can use any road, highway, or parking lot in your vicinity.
Next, after you have picked out your new old car, spend some time getting to know it. Before any artist creates a masterpiece, they must know their materials. You must learn as the artist, how the car reacts to any situation, before you can create your masterpiece. Know the stopping distance at various speeds, in different types of weather. Know its turning radius. Know its top speed, gas mileage, everything you possibly can about the car. Then you will truly be ready to create a great work of art, safely.
Car characteristics fall into five main categories, internal appearance, external appearance, body structure, noise pollution, and improvised repairs. These categories are interrelated, and some I will cover together. Mixing the different types of damage, both slight and major, will allow you to create your ideal vehicle. Remember that you're not trying to destroy your vehicle completely, only partially. The line between just enough, and too much is thin; an undriveable car is no use to anyone, and will make you look like an idiot.
First, go after the interior. It's quick, it's easy, and you can do it in your driveway. Start by leaving the windows partially down when it's raining, this will help with the smell. Maybe put some Altoids, some Tums, a little bit of Ex-lax, and maybe even some Tylenol in the back too. The rain will dissolve the tablets, and make your carpet lots of different colors. Try putting small cuts in the seats; don't make them too big, you want them to look accidental, and let them grow. You can throw food in the back too, but I warn you, the smell is awful. The key is taste. Don't do too much, or you'll look like a poser who only tries to have an interesting car.
The next two categories are very similar, so I will cover them together. The exterior is tricky; too much damage to the exterior and/or structure of the car, and you may not be able to drive it. This would defeat the whole purpose. So be careful, be creative, and drive insanely, safely.
Okay, now it is time to work our creative magic on the outside of your beautiful car. I have two words for you. "Hit Curbs!" Hit lots and lots of curbs with your car. Everywhere you go hit a curb. In the parking lot of the supermarket, hit a curb. When you're at church, and nobody's looking, hit a curb. Hit so many curbs, that you get sick of them. Hit 'em till you wanna puke. Hit curbs till you just can't take