I'm using an Arduino Uno, which I've programmed as a bike computer. I wanted to add a button to pause the LCD so data can be collected from the screen.
I put two pins of the button on a 5V rail (on a protoshield) and connected one of the others to digital pin 10. I think programmed the button just to control the LED on the board. When I turn the board on, the light is always on without me even touching the button. I tested continuity and pin 10 shouldn't be getting any power at all but it is.
No pull-down resistor?
Digital inputs don't take power, then sense voltage without taking any current (*)
(*) well a little, measured in picoamps
When nothing is connected to an input that pin can read high or low at any time. This is called a floating input.
To attach a button connect the button to make contact between the input pin and ground. Then in setup enable the internal pull up resistors with a pinMode call.
For more information see:-
http://www.thebox.myzen.co.uk/Tutorial/Inputs.html