Use a tripod. Some of the best shots are around sunrise and sunset -- there isn't a lot of light. If you notice your camera shake when you hit the shutter button, set a 2 second delay. Tap the shutter then move your hand away from the camera. The 2 second delay lets it stabilize before the picture is taken.
Don't use a flash.
Since you want to take a picture of a CAR and not a landscape, find an area with nothing but sky in the backdrop, like a field or a massive parking lot with no lamp posts.
If you can't find an area with nothing in the background, then find an area that will give some backgrounds which complements the car. This will require you to have a better eye for composition.
If you have a background, don't keep shooting on the same spot. Change the composition. Move the car around, shoot from the other side, etc. If keep shooting on the same background, all your pictures are going to look very similar since the background is a major part of the composition.
You can also use a zoom lens and take advantage of the telephoto effect and narrow depth of field to turn a busy background into beautiful bokeh.
Here's an example:
This is a similar shot with a wide depth of field. The background can be distracting.
Start early. The best hours are around sunrise and sunset. Start an hour early so you can get warmed up taking photos and figure out where to position the car, and what angles it looks good at. As the lighting improves, you'll be ready for it and your pictures will improve.
Some cars were originally designed as a sketch from one angle. Find that angle and make sure to get a good shot of it. If you're taking advantage of natural lighting, shoot each angle at various times during the shoot, so that you can pick the best lighting for each one.
You don't always have to include the whole car in the shot.
Other people mentioned headlights... You DON'T have to turn the headlights off to get a good picture, but you do need crystal clear lenses and, preferably, projector headlamps. Otherwise you'll get a lot of scatter from the lights, and lens flares all over the place.
Stay out of the range of the lights where they cause lens flare or starbursts (or open your aperture more so they aren't so bursty). Remove any filters to reduce the glare and lens flare if you're shooting the lights.
The headlights are in these pictures, and I didn't use exposure bracketing to make any sort of composite.
Sometimes you can use natural lens flare to get an interesting, cinematic look:
EDIT: A note about polarizing filters... because of the shape of the car, one filter angle is going to eliminate reflections on the side of the car, and another filter angle is going to eliminate reflections on the top of the car (and the windshield). There is no setting that will eliminate both. One way to use a polarizer when shooting a car is to take at least two shots without moving the camera (obviously you need a tripod for this), with different polarizer angles, then make a composite of the images in Photoshop or GIMP, so that you can eliminate the reflections on all the windows and/or the hood and side of the car.
My 2c, you don't have to use a tripod when it's dark, depending upon what's around and how resourceful you are. I took a few lovely shots of Wellington city (NZ) using my jacket to support the camera on a handrail for "long" 15 to 60 second exposures. Works well, the only criteria is no gradual movement as the fabric slowly deforms under the load, and no vibrations in the structure you're on. I often use the strap to rest the lense and base on to level it up or gain the right attitude to the world, folding it for more thickness, using the unpadded bit for less, etc. A small fabric bag full of rice is a good option with some control afforded. Here's a ground+strap photo of my 740 at my sister's wedding:
And earlier in the day framed for the tree:
And a few other random shots I quite liked, all taken with my GF1 with the big lense that doesn't have a very good fstop.
I should go to bed. And yes, I know some of them are a bit crap in various ways, but they're also kinda nice in other ways
The maroon 740 wagon was for sale recently, I talked the seller out of selling it So I can buy it later when they redecide to sell it...
I honestly prefer using my smartphone on taking photos nowadays. Whenever I need to use my camera I have to make sure that the shutter speed, ISO, and other technical things are in proper setup to ensure that I will get quality photos.