Today's automatic transmissions are so good, shift so effortlessly, and do their job so invisibly that you can't blame someone for thinking they won’t break. However, these are still man-made machine parts and they do wear out and break down if we don't take care of them. To prolong their function, here are some bad habits to avoid with your automatic transmission.
1) Shifting into the opposite direction while the car is still moving (reverse into drive or vice versa). Sometimes we're in such a hurry that we tend to shift into drive or reverse while the car is still moving in the opposite direction. Although there are systems in place that will tolerate acts of this nature, it still contributes to premature wear of the transmission's clutch packs and bands. The best practice is to come to a full stop before you select reverse or drive.
2) Revving the motor in neutral and then slamming the shifter into drive. This is called a "neutral drop." Don't do it! Sure, you might be able to do burnouts this way, but be prepared to have your transmission repaired. By doing this, you're putting a lot of stress on different parts of the transmission—pressure that the clutch packs and bands were not designed to withstand. Chances are you'll break your transmission by doing this. The best thing to do is to not rev your engine before you engage Drive.
3) Shifting into park while the car is still moving. You can do this a few times and it won't harm your transmission. You'll probably only hear a few clicks and then your car will stop. There's a part in your automatic gearbox called a parking pawl which is a pin that engages a notched ring attached to the transmission's output shaft. The pin is spring loaded, such that it will skip engagement if you're still moving. However, if you do this enough you could damage that pin. The proper thing to do is to come to a complete halt before you put your transmission into Park.
These days, most automatic transmissions are quite robust and can take a lot of punishment. You don't really need to do much in terms of learning how to use them. Just avoid the three foregoing bad habits and your transmission will have a long and healthy life.