Uncovering the ID is a simple process, but it's not particularly obvious. Here are the steps:
Open iTunes and click on your iOS device in the left pane (fig.1)
Make sure the Summary tab is selected (fig.2)
Hover your mouse over the "Serial Number." Click once. The serial number will change to "Identifier (UDID)" and reveal a long string of numbers and letters (fig.3)
You can't highlight the UDID string, but you can still copy it to you clipboard by pressing Command-C on a Mac or Control-C on a PC. (fig.4)