Okay The simplest answer is that you can't just take a flat art file such as the one you posted and make it 3d. It's just not designed to be manipulated in that way. So the first thing you are going to need (and everything should be available in the downloads section on this site and if not then easily obtained from other sites) is the 3d model. A Render Scene. The ones used in Nr2003 are typically set up for use with 3DS Max software. You will also need the templates specific to the mod used with the render scene. Those are generally in Photoshop PSD but also come in other formats like Gimp. These are not designed to be used in Illustrator although I personally have opened the PSD files in Illustrator for some designs. You will also want the Carviewer software and to download the .X files for carviewer for the mod you want to render. The carviewer software will take a flattened image you save out of photoshop in a Bitmap or TGA format and display it for you on the 3d model that we painters like to use to check our alignments and look for warping issues that we might have to manually fix.
Then in photoshop you can start to transfer over the layers of your design from Illustrator into the template in photoshop. It will be a bit of trial and error for you until you get it just right. It's not difficult once you get used to the unique differences in the template such as rotating the numbers a couple of degrees to get them to orient properly, adjusting the stroke width of a line to make it line up properly around a corner or shifting a section of art around to get it to line up where you really want it. If you look at the layout view that you shared, that car is displayed in a bit of a 3d view already. whereas the template in Photoshop doesn't really show the depth and distortions in the same way. PRACTICE PRACTICE PRACTICE. It will get a little easier to work around each time.
Once you have finished layering your ar in photoshop you can then save it as a psd with layers so that you can go back and make further adjustments or revisions and then flatten the image and save as a Bitmap, TGA or JPEG (I recommend jpeg for renderings) then open up the model in 3dsmax. use the tools provided to align and rotate the car until you have the angle and view you would like to display. Press the M key to bring up the materials section. Find the bubble that has the textures for the car you want (mustang, Camaro, Camry etc) then select the (I think it's diffuse) material but its the primary design layer of the model. import your paint onto it and the screen will preview it for you. then close the material window and press (f10 I believe it is) adjust the image size settings to what you want and at the bottom of that window click render.
Give it some time and when finished you can save it as a jpeg.
Now, I realize that sounds like a lot of steps and it is but once you get the hang of it you will find ways to improve the workflow that best suits you and you will be able to play around with different settings and such to get different results.
Additionally, if you can't get 3dsMax you can always submit your car flat to the ModSquad or in our own render request forum right here at Stunod and, it might take a bit to get to it but the guys are really cool and will usually render the car for you.
Just make sure that if you are posting the designs somewhere that you give proper credits.
Most of all, HAVE FUN!
