The following is a beginner's approach to learning how to double - clutch. This technique allows downshifts from higher speeds without any synchroniser wear. This is VERY important if you ever want to drive really quickly and keep your transmission intact for extended periods! 

The Easy Way to Double-Clutch 
By Jeff Krause. 
Double-clutching is the proper way to downshift at speed without placing excessive wear on the transmission's synchronizers. This allows you to select a much lower gear without the tell-tale lurch you normally get when the clutch is let out after downshifting. 
When downshifting my BMW M5 from 4th gear to 2nd at 50 mph, I need to raise the engine speed from 2200 rpm to 5000. To prevent excessive synchroniser wear, the clutch is depressed and the shifter is moved to neutral. The clutch is then released, and the gas is depressed to bring the engine speed up to where it needs to be for the lower gear. The clutch is then depressed again and the shift lever moved into the lower gear. When the clutch is released the second time, the engine is already turning the proper speed . While this sounds complicated, it's easier done than said, and only takes about a second. 
To better understand how the process works, a little background on transmission fundamentals will help. 
A typical transmisson has two shafts, one connected to the engine through the clutch, and one connected to the rear wheels. There are usually four to six sets of gears on these shafts and they are selected with the gearshift lever inside the car. When changing gears, the clutch is depressed to disconnect the engine from the transmission so there isn't any stress on the moving parts. Since the output shaft is permanently connected to the rear wheels, the only way to match the speed of the two shafts is to use the throttle to adjust engine speed. 
Once the engine is turning the right rpm, both shafts will be turning the same speed, and the gear lever will fall into gear WITHOUT using the clutch! (Although most of the time you are shifting too fast to be that accurate) 
EXCERCISES 
1) With the car idling in neutral, slowly step on the gas until the engine is turning 3500 rpm. Do it again bringing the rpm's up more and more quickly until you can give the pedal a quick stab and have the revs stop where you want . As you shorten the time allowed to match revs, you will notice it takes more throttle. In fast driving, you will be shifting so fast 4 will take full thottle! Now try matching revs at 4000 rpm. 
2) Find a deserted road, and maintain 40 mph in 4th gear. Now shift into 3rd, and see how many rpm's the engine speed increased. At this speed, the difference won't be very much - maybe only a few hundred rpm. Go back into 4th gear. This time put the clutch in, push the lever to neutral and let the clutch back out. You are now coasting with the clutch out. Raise the engine speed to where it will be in third gear. Quickly push the clutch in, select 3rd gear, and let the clutch out. There should be no perceptible lurch if you accurately matched revs. Try the same thing at higher and higher speeds. As the road speed goes up, the speed difference between gears will go up as well. When going from 5th to 3rd a highway speeds, you may end up within 1000 rpm of redline. The easiest way of determining your maximum downshift speed is to watch the tach and speedo as you are shifting up at redline. If you shift at redline from 2nd to 3rd at 60 mph, subtract 10 mph, and that becomes your effective maximum downshift point for 2nd gear. If are within 10 mph, you are better off staying in the higher gear. 
HEEL-AND-TOE DOWNSHIFTS 
This combines double-clutching and braking into one event. Place your foot on the brake as far to the right as you comfortably can. While braking, roll your ankle so you can catch the left edge of the gas pedal with the right edge of your foot. If the pedals are too wide, try placing the ball of your foot on the brake, and the heel on the gas (This is where the term heel-and-toe originally came from). Now try gently slowing down and downshifting. With practice, you can brake hard and downshift in one smooth motion. This will prevent the wheels from locking when the clutch is let out in the lower gear, and you will be ready for a burst of acceleration coming out of your favorite corner! 

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am used to double clutching all of my shifts, and I find it helps with the heavy flywheel of the A4. 
Practice this slowly, and then as you get the hang of it, work your speed up. 
Start off in first, and accelerate up to say, 4,000 revs in first. Hold it there, and make note of the road speed. Now shift into second, and get back to the same road speed in 2nd. You know know the rev drop between the two gears. 
Start off in 1st again, and as the revs hit 4,000, let off the gas, push in the clutch, and slip the lever into neutral. You are now coasting & losing speed, but don't sweat it. Let off the clutch pedal, still in neutral. Rev up/down the engine as needed to get to the right revs for second gear, push in the clutch, slip the shifter into second, and let out the clutch. 
1-2 is the toughest shift because all of that gear reduction means the flywheel effect of the motor, and the compression braking are exaggerated. Once you have the hang of this, try the same exercise in 2-3 3-4, and 4-5. 
Down shifting is just the reverse process. Let off the throttle, clutch in, slip into neutral, rev it up a bit to the higher revs required by the lower gear, clutch, and slip it in. 
There are fiery debates as to whether double or single clutching will be harder on throwouts, clutches and synchros. My answer: Don't worry about it. Do what feels comfortable. These cars should last a long time regardless of method if you are gentle. 
My problem is the shift mechanism itself I am not used to yet, so I sometimes find myself hitting between gates, rather than the gear I want. I stuff the lever between 5th and 3rd, and have to back off and try again. Only a problem in panic situations (A daily event here)