How do I prevent the "Super" button from opening the dash?

One way to achieve this is to use CompizConfig Settings Manager.

It does not come preinstalled with Ubuntu by default, so you probably have to install it first:

sudo apt-get install compizconfig-settings-manager

Alternatively you can also click this link to install it through your Software Center: Install

When it's installed, launch it with the command ccsm or search it in the Dash.
You will see a window like this:

Select the Ubuntu Unity Plugin, then switch to the Launcher tab in there.

The first option is what you're looking for:

Key to show the Dash, Launcher and Help Overlay

You can set a new shortcut or entirely disable it using the three buttons on the right.

I suspect you want to stop Ubuntu/Unity from intercepting the Super key (which is the key with the Windows logo on it). One possible solution would be to install the unity-tweak-tool as suggested in this question:

sudo apt-get install unity-tweak-tool

Launch the unity-tweak-tool. In the 'Unity' section, select 'Additional'. Click on 'Super' next to 'Show the launcher'. Now you can select a different key or key-combination.