Society of Robots has a great video of a robot arm-clocks -
The robot arm is probably the most mathematically complex robot you could ever build. As such, this tutorial cant tell you everything you need to know. Instead, I will take shortcuts and just talk about the bear minimum you need to know to build an effective robot arm. Please bear with the math . . . enjoy!
To get you started, here is a video of a robot arm assignment I had when I took Robotic Manipulation back in college. My group programmed it to type the current time into the keyboard . . . (lesson learned, dont crash robot arms into your keyboard at full speed while testing)