How do I make animations like this?

Hello everyone, I am trying to learn how to make motion animations like this: Yoochan Shin, Republic of Korea, Finalist: 2017 Breakthrough Junior Challenge - YouTube

I have motion v2 btw.

I am trying to make an animation where I can use my art from adobe illustrator to move around like what you see in the video. For example the first sequence where all the lights move to the left, how do I do stuff like that? I have been trying to find tutorials all over the place but I cant.

Thank you