You can either run wires between the BlinkM and Arduino, like on a solderless breadboard, as in (a), or you can plug the Arduino in directly as in (b). BlinkM plugs into the Arduino's pins 2,3,4,5. You can use the BlinkM_funcs.h library to turn two of those pins into a power & ground.
Notice the (Black, Red, Green, Blue) color coding of the BlinkM connections. I find this to be a useful mnemonic for remembering the order of BlinkM's pins.