The very first thing to check is to have "Advanced Driver" switch ON.   If this switch is off, only the audio ports function and the UA-20 will be using the OS X standard USB audio driver.  The problem there is that in both DP4 and Cubase SX these generic audio drivers are not detected properly.

With the advanced driver switch ON, the user must first unplug the UA-20 then download and install this driver:
download.edirol.com
Restart the Mac and Launch DP4. In DP4, choose "Open Audio MIDI Setup" from the SETUP menu, and click the "MIDI Devices Page". AMS should automatically detect the the UA-20, then simply click Add Device to configure your MIDI devices. Chapter 4 of the DP4 Getting Started guide contains a more instructions on configuring MIDI.