Hello, and how do I move an object's position up and back down again to Audio Amplitude?

The principals are all the same. Turn the change in Audio Amplitude - Both Channels (or left or right), into values for one or more properties using a linear or ease interpolation method. The expression is going to be the same up to the point where you get to the array at the end. 3D layers have 3 spots for Anchor Point, Position, and Scale so the array looks like this [xValue, yValue, zValue]. Change the layer to 2D and you only have two values in the array. Colors have 4 values so they look like this [0 to 1 for Red,  0 to 1 for Green, 0 to 1 for Blue, 0 to 1 for Alpha]. There are a lot of properties that have only one value. Rotation is an example. 

The expression always starts by declaring a variable that looks in a Comp, then for a Layer, then for an effect or other element like the Range Selector for a text animator, then the property that has a value. When you have defined the property using that hierarchy you can then apply that to a linear operator. For example:

t = thisComp.layer("Audio Amplitude").effect("Both Channels")("Slider"); 
tMin = 0; //minimum Both Channels Slider value
tMax = 30; //maximum Both Channels Slider value
value1 = 0; // minimum starting value to output
value2 = 200; // maximum ending value to output
NewV = ease(t, tMin, tMax, value1, value2);

[value[0], value[1] + NewV, value[2] * NewV]

I chose t, tMin, tMax, value1, and value2 for the variables because when you choose the Expression Language Menu>Interpolation>ease function you get the text I used for NewV. You can leave off the tMin, tMax, value1, and value2 variables and just enter numbers in the ease method if you like but it makes it easier to explain how this expression works. 

Apply that expression to the Position of a 3D layer and the Position values for X, Y, and Z will not start to change until the value of the Both Channels slider moves above zero. The expression will move the layer up to 100 pixels in Y and multiply the original Z position by 100 as the audio levels change from 0 to 30.

The easiest way to figure out what the values you should use for tMin and tMax is to look at the graph editor.

That explanation should solve your problem, Just match the array to the property you want to animate and set value1 and value2 to the minimum and maximum amount of movement.

Hi! Welcome. You'll want to right click your adio layer go to Keyframe Assistant > Convert Audio to Keyframes. That will create a new layer called something like Audio Amplitude. After that you will want to define the range of amplitudes. Here's a pretty good tutorial: https://www.youtube.com/watch?v=k6xZUlhlZxs