Well if you have El Cheapo camera then your options will be a bit limited anyway than if you have El Magnifico camera with all the bells and whistles. Just pointing and shooting in auto mode may work great anyway but I would try the following methods if your camera allows it:
1) Take pics without flash - this should force the camera to let more natural light into the lens and allow your LEDS to stand out more
2) Select any 'night portrait' mode that your camera has - same as above - you will need to keep the camera still for longer in this mode. Use a tripod, brick wall, some sort of support to help.
3) Select 'shutter priority' and reduce the shutter speed - for expensive cameras - same effect as above but with much more control as you can adjust the shutter speed until you're happy with the effect.
4) Select fully manual if you have a fully manual SLR or prosumer digicam and adjust the shutter speed and aperture as appropriate.
One last note, if you zoom in at all then you'll reduce the amount of light getting into the cameras (unless you happen to have a really expensive lens and if you had that you wouldn't be asking here!) so don't zoom in.
Shooting at night is always a problem with LED's. You will either end up with seeing just the LED's and not the car or the car and the LED's will be overexposed.
Best thing is to try and aim for the "Golden Hour". This is the period of time after sun set (or just before sunrise if you get up early enough), where you get a great light show from your LED's but there is still enough light to get a decent exposure on the car.
Regardless of camera as they are all different and all have different types of exposure control, if you can shoot without flash, all the better but this will make for quite long exposure times which will ultimately suffer from camera shake.
If you can use a tripod all the better and a cable release for the shutter is even better as well. A good trick is to set the camera up on a tripod/wall/chair or some other immoble steady surface, set the camera for the timed shutter release, the sort of thing when you want to get a pic with yourself in it.
Set it all up, set the timer and then set it off. This will allow the camera to take a good shot without camera shake induced by you holding it or pressing the shutter release button.
Hope that all makes some sense.
That is the technique I used to get some of my shots like this
One of the best"Golden hour" pictures I have seen is that of Webber and his car. The car and the wall are nicely exposed and the blue neon glow is visible without being overexposed. Perfect.