Start by learning how to create keyframes from audio using the Keyframe Assistant. Then learn how to use the Expression Language Interpolation methods like linear and ease. Plug the minimum and maximum values from the Audio Amplitude layer slider of your choice by checking the Graph Editor and looking at the Value graph. Choose the minimum and maximum values you want to use for the effect or property that you want to animate and enter them in the Linear method and apply that expression to the property you want to animate.
If you wanted to use the Audio Amplitude/Effects/Both Channels/Slider to drive your animation you would set t equal to the slider using a simple pickwhip.
Let's say your Audio Amplitude layer returned values from 0 to 30 and you wanted the animation to start when the value passed 5 and reach it's maximum value when the value passed 25 so you catch all of the beats. Now you have the tMin and tMax values for your Linear expression.
Let's say you wanted to animate the Y position of a shape layer and have it start at its original position then bounce up 400 pixels when tMax hits 25. Now you have the value1 and value2 numbers for the expression.
Here's what the expression applied to Shape Layer/Transform/Position would look like:
You work the same kind of magic with opacity, color, rotation and you start building the composite one effect and one layer at a time.
There is no single plug-in you can just add to a layer and generate the kind of animation in the video. Everything from opacity, maps, position, distortion, and just about anything else can be controlled with these kinds of expressions.