Hi Mike
Arduino programs are written in the C programming language. ( You can also use a more advanced language called C++ but, to begin with, C should be enough). So, part of the answer to your question is to find books or online tutorials about C.
However, the Arduino comes with specific functions built in to allow your C program code to access the hardware features of the Arduino, like the input and output pins. You won't find these mentioned in a generic C tutorial, but they are explained in the Reference part of this website.
A good place to begin, though, would be with the example programs in the Tutorial section http://arduino.cc/en/Tutorial/HomePage. Start with the easy ones and work through them to understand what each part does. You will start to pick up the C programming language.
The example programs are also contained in the Arduino IDE (integrated development environment - long name for the software you use to write Arduino programs and load them onto your Arduino) which you can download from this website.
Then, try making your own changes to the example programs. For example, if you have a program that flashes the onboard LED on the Arduino, try changing it to flash faster or slower, or to alternate long and slow flashes.
Hope that helps
Ray