basic question..

hi,

never used one of these before, so very basic question:
once the program's been sent to the board, does it need to stay connected to the computer to run?

thanks..

No, once the sketch/program has been uploaded to the arduino it does not need to be always connected to a computer. Depending on what arduino you have you can power it in many different ways (USB, Battery(DC jack, JST connector), DC jack from mains power).

perfect, thank-you