Arduinos come in two flavours - 3.3 volts or 5 volts. Traditionally digital systems have run on 5V, so this is suitable for designing with older sensors. More recently the quest for lower power usage has driven a shift to 3.3 volts.
Some Arduinos are dual-voltage, and can be switched between 3.3V and 5V, but be careful as connecting a 3.3V sensor to 5V is likely to damage it.
Supplying power to an Arduino is easy. The easiest way is to connect the Arduino to a USB port on your PC or laptop. The power provided by your USB port is then used to power the micro-controller and supporting electronics. Only limited power (500MA usually) is available from a USB port, so do not try to connect motors or other power hungry devices.
If you would prefer not have your Arduino connected to your PC it gets only a little bit more complex. Most Arduinos have a 'raw' power input, that can take power from about a volt higher than the board's PC operating voltage, and regulate it to meet the Arduino's requirements. The built in regulator is usually designed for low power operation, so power hungry devices such as servos or motors can not be powered directly by the Arduino, but must be powered by an other power source.