Since no one wants to put this in as an answer...
First, you need to install the Desktop Experience feature using Server Manager, or with the following command line:
ServerManagerCmd -i Desktop-Experience
This will install the Windows Aero and other desktop themes, along with a lot of other programs that go into Vista by default (Windows Media Player, Windows Photo Gallery, etc.).
Next, you need to set the Themes service to Automatic and start it.
If you're running Windows Server 2008 (not Windows Server 2008 R2):
Click Control Panel > Personalization
Click Windows Color and Appearance and select the Windows Aero color scheme
(To turn Aero off, click Theme and select the Windows Classic theme)
For Windows Server 2008 R2:
Click Control Panel > Appearance and Personalization
Click Personalization and select the Aero Theme