Go to Admin Menu > Appearance.
The Appearance screen contains a list of all of the different themes that are available on the site.
Locate the Adminimal theme.
Click the Adminimal theme's Install link.
A confirmation message will appear at the top of the screen when Adminimal is successfully installed.
Scroll down the screen.
Administration Theme select box = select Adminimal.
Click the Save Configuration button.
The theme will change nicely, but the menu will hang on to its original styling, which doesn't look well (at best) and is inaccessible (at worst).
Go to Admin Menu > Extend.
In the filter box, type adminim.
When the Adminimal Admin Toolbar module appears, check its box.
Click the Install button.
The change to the menu will appear instantly.