Check out http://www.designyourowncar.org/ . It has all the ways to design cars since "design" is such a loosely used word. Customizing, modeling, software, sketching, building, and playing games are all mentioned as well. Good luck.
Designing your own car online can be really exciting, being able to pick the color of the car, wheels, rims and many other features. Some websites even allow you to race people with your custom made vehicles. To find more information click here: http://www.guzer.com/games/createaride.php
The best site I found to design cars online is called Designer Space. You have cool tools such as choosing your car, making a portfolio of all your creations, and even entering contests for your designs. You can find more information here: http://www.designerspace.com/index.php
If you want to just design a car wrap I found this site http://www.custom-car-wraps.com/ it lets you pick a car close to the car you want and then design a wrap for the outside of your car (those vinyl wraps on cars). It is free I did a logo and some letters and after you make a mockup design they let you search for a wrap shop nearby and you can just find wrap shops near you if you want to do something else like chrome or matte black (I think matte black looks really cool)