There are many ways you can power your Arduino board. The important thing to remember is to use the correct voltage with the right method and board. Some Arduino boards, for example, the Arduino Mini, can come in a 3V flavour and can be blown when using 5V. The Mini also comes in a 5V flavour here.
Usually, you can check this by looking at the onboard volt regulator id or serial number. If it's 5V, then use 5V if its 3V then, well, yes use 3V.
The two most common ways to power your Arduino is to use the onboard USB port and USB cable or use the built-in 9V battery plug. But this is cumbersome when building something that requires movement or with no access to USB power. In the case of robotics, you will usually have a high voltage battery source, i.e., 12V and up, and want to use this source of energy to power motors as well as your Arduino. To do this, you can look at two other power pins on the Arduino.
- The 5V pin - Takes 5V in voltage as well as can power other boards/modules that have a 5V rating. Remember that this only takes 5V, any higher and you risk blowing the Arduino as well as all boards connected to it. Using a voltage regulator here can create a safety net, but then you might as well use the Vin pin.
- The Vin pin - This takes 7V-12V. Using this pin is your best bet for a one power source method. Remember that above 12V you will have to use some voltage regulator to bring it down to 12V first.
Some motor driver boards, come with a 5V regulator built in. This allows you to power your motors with higher than 12V power supplies, and then run 5V from the driver board to your Arduino board.
Remember when doing this sort of thing, not to combine circuits, and make sure your groundings are correct or you will get the bad smell of burnt circuits.