Regularly check your parking space for leaks and if you see any, get it fixed before lack of oil or fluid can cause expensive problems.
Once in a while check the transmission fluid level and condition. However, not all cars have the automatic transmission dipstick; in some cars, for example, in late Volkswagen models, the transmission fluid can only be checked by a mechanic in the repair shop. You can check your owner's manual for instructions to check the automatic transmission fluid. If the transmission fluid level is too low, there is a leak somewhere that needs to be fixed. Change the transmission fluid as often as it's recommended in your owner's manual or when it becomes too dark (rather brown than red) or dirty.
Use only the same type of transmission fluid as specified in the owner's manual or on the dipstick. Many newer vehicles are very sensitive to the fluid type. For example, the owner's manual for 2008 Honda Civic says "Using transmission fluid other than Honda Genuine ATF-Z1 may cause deterioration in transmission operation and durability, and could result in damage to the transmission". Never shift to the Reverse or Park modes until the car comes to a complete stop. Don't shift the transmission from 'Park' to other modes at high engine RPMs.
In many cars, the automatic transmission can be damaged if towing with the drive wheels on the road. If you have to tow your vehicle, check your owner's manual for the proper way of doing it. If you planning to tow a heavy trailer with your vehicle, consider installing an additional transmission fluid cooler. It's also good idea to change your transmission fluid more often when towing a trailer.
