You could do it with a laser, but it would drive you and your assistant nuts, especially if you don't have an assistant.
On level ground, put a blank canvass in front or behind your car. The canvass could be the drywall at the back of the garage or cardboard or anything for that matter as long as it is a flat surface and large enough.
The someone at the other end shines the laser at the edge of the cars surface, where the laser disappears, the assistant marks a dot. The laser has to stay parallel and level the whole time. The level part is easy, just mount it on a 4' level. The parallel part would be tougher, but you could draw parallel lines on the ground and use a jointed parallelogram base for the level. Just make sure it always in line with grid lines.
It would be a ton of work, but you'd get a nice profile on the canvass that could be measured pretty easily!
I am impressed by the talent displayed in these posts. My way is pretty simple-minded...
I did a google image search for a Beetle (my car). Most cars have pictures on-line that are straight-on front views. I got the height and width from car dimensions. Then, I printed the car picture onto a sheet of graph paper stuck in my printer. I counted the number of squares in the image and used horizontal and vertical scale factors to get the area. Yes, different scale corrections were needed since the picture was distorted by somebody to make it look more sexy.
The number I got: 23 square feet for my 2003 New Beetle.
So, I have a technical question-- should the area under the car be counted as part of the frontal area?
Now, why do we need the frontal area? ANS: drag coefficients are routinely published but frontal areas are not. You need CdA to calculate the drag.
Measuring CdA directly (measuring the drag) is a fairly easy thing to do. Start with the easy formula--
F = m a = CdA 1/2 rho V^2 + Crr m g
Rho is air density. You can get that with the help of the airport-- they can give you pressure and temperature and may have the density as well. In metric units, it will be about 1.2 kg /cu.meter. V is the speed of the car in meters per second: mph x .447 = meters /sec. m is the mass of the car in kilograms. 1 kg = 2.2 pounds. Crr is the tire rolling resistance coefficient, which you will find out in the calculation. And, g is the gravity constant, about 9.81
Take your car out to a level, straight section of road when there is no wind or traffic and no cops are around. Take a stopwatch or something like runners use. Go as fast as reasonable, say 80, shift to neutral and start coasting. Start the watch when the speed crosses 75, then click it at 70, 65, 60, 55, 50, ..., 25, 20, 15, well, maybe 10. Do that both directions about three times and average the numbers. Then, carefully check your speedometer and correct the gage readings to true speed. Now you have a good set of numbers.
Make a graph of speed versus time. Take your car to an accurate truck scale and find out how much it weighs. Have the scale operator do it both with you in the car and out. The difference should be close to your correct weight.
Okay, the slope of the curve is the car's acceleration, a = F /m. Draw a straight line tangent to the curve at a very high speed, say, 60, and at a very low speed, say, 20. (Don't worry about where the straight line touches the curve, just read the speed where it does.)
Now you have all the stuff you need to calculate CDA, which will be in square meters.
Can you guess a value for either CdA or Crr? CdA will be around 0.7 sq.m. Crr will usually be in the range from 0.012 to 0.007, depending on the quality and condition of your tires and their pressure.
You might plug all your numbers into the equation at the low speed tangent, with a guess for CdA = 0.7 and calculate the only remaining unknown, Crr. (The answer isn't sensitive to your guess for CdA at low speed.) Then, plug that into the high speed case and calculate the CdA. (Which isn't sensitive to Crr at high speed.) Go around one more time, plugging in the new CdA, etc., and the calculated numbers should begin to "converge," repeat themselves. And, then you have both the CdA and the Crr for your car.
The numbers for my car:
Crr = 0.0065
A = 23 sq.ft.
Cd = 0.30
I have very low rolling resistance tires and I have a drag reducer to bring down my Cd. There are pictures at www.max-mpg.com