Basic tips.

1. Always step on the brake when shifting from P to any other gear. Some cars wont even allow you to shift without steping on the brake pedal.
2. Normal driving, just shift to D and you are set.
3. P = park. Always set to P when you park the car. Dont use this gear when stuck in traffic. Better to put in N or neutral and set hand brake. BTW, most modern AT wont start if you are not in P or N.
4. R = reverse.
5. N = neutral
6. D is drive. AT will shift between 1st to 3rd or 4th gear as needed.
7. 3 means your AT will shift from 1st to 3rd gear only.
8. 2 means your AT will only shift between 1st and 2nd gear. Useful when climbing hills and engine braking while going down hill.
9. L or 1 = 1st gear only.
10. OD or overdrive. on cars equipped with OD, keep it on while driving. It will give you better FC. When you need more power, like overtaking or going uphill, turn it off and you will get more power. Its kinda like a final gear on ATs.
11. You can make an AT shift by using the gas pedal. Flooring it will make you downshift. A quick step and release will make you upshift.
12. When coasting, keep the car in D and just keep your foot off the gas pedal. Dont ever shift to N while car is moving. I'm not 100% sure but I read before that it cuts off supply of ATF and can cause damage to your tranny. So better safe than sorry.

Do a search, there are a lot of topics on AT. I also suggest you read the stick on automatic transmissions. Its very informative. I also posted the proper way to check your ATF, just search for it.

The best way to take care of your AT is by using the correct ATF. Keep it at the right level and change when needed. ATF change intervals should be in the manual.