If you replace the batteries in your VW Passat's keyless entry remote, or if you purchase a spare key, you will likely need to (re)program it to get your Passat to obey its signal. Your Passat's manual may have the programming instructions or may merely tell you to have your local dealership do it. However, your goal is instead to save yourself the expense, since the dealership will charge you for this service.
Put the key into the ignition. Turn it to the "On" position but not so far as to start the car.
Lock the driver's door with a second key. You can do this from outside the car.
Press the "Open" button on the keyless remote (smart key) once. The car will sound its horn to confirm that you have done everything correctly so far. Wait six seconds, and press the "Open" button once.
Remove the key.
Repeat the above steps for each successive remote. However, the first time you press "Open" for each remote, you have to press it one more time than you did for the last remote you programmed. For example, for the second remote that you program in one sitting, you'll press the "Open" button twice. For the third remote, you'll press "Open" three times. Continue in this fashion.
You must switch off the ignition between codings of different remotes. These directions are specifically for a 2004 VW Passat. They may not work for all years. If they do not work for your car, then you may need to call around to different dealerships to see if someone will tell you the instructions for your car's year. Otherwise, you'll have to take the car to have the dealership program the remote for a charge.