I will explain it in more detail for you when I get more time, but just to get you started, you need to animate the individual points on the shape using the path key frames.
See in image below, Shape 1 > Path 1 > Path.
Using the key frames in that line and with the pen tool active, manipulate each of the individual anchor points on the arrow.
They can also be grouped and free transformed together using a combination of modifier keys (shift, Alt, Ctrl).
Its still very new to me, so not sure the exact combination of the top of my head.
I did a lot of experimenting using masks and having them appear from under a mask to start with, but that was nowhere near as good as this method.
To get it moving smoothly and looking good is going to take a lot of practice and patience I think.
Will know more tomorrow hopefully.