Ever since the dawn of Arduino, one question has been asked over and over again: "what kind of DC adapter can I use to power my Arduino?"
The short answer is: 9 to 12V DC, 250mA or more, 2.1mm plug, centre pin positive.
The long answer is that an off-the shelf Arduino adapter:
These important details are often contained right on the adapter. Here's a picture of an adapter ideally suited to powering the Arduino. The important info is underlined in red here:
As you can see, it has all the right stuff: 12V, DC, and a little picture that shows you that the middle pin is positive.
Current rating: Since you'll probably be connecting other things to the Arduino (LEDs, LCDs, servos) you should get an adapter that can supply at least 500mA, or even 1000 mA (1 ampère). That way you can be sure you have enough juice to make each component of the circuit function reliably.
One final note. The Arduino's on-board regulator can actually handle up to 20V or more, so you can actually use an adapter that puts out 20V DC. The reasons you don't want to do that are twofold: you'll lose most of that voltage in heat, which is terribly inefficient. Secondly, the nice 9V pin on the Arduino board will actually be putting out 20V or so, which could lead to potential disaster when you connect something expensive to what you thought was the 9V pin. Our advice is to stick with the 9V or 12V DC adapter.