Thanks to all who responded.  The solution is:

Private Sub UIButtonControl1_Click()
    Application.Caption = "Here is my new caption"
End Sub

When the button to which this snippet is attached is pressed, the text on
the upper left of the ArcMap application window will read, "Here is my new
caption."

Thanks all.

Gary Ostroff, P.E.
Sr. Project Manager
HydroQual, Inc.
1 Lethbridge Plaza
Mahwah, NJ  07430
201.529.5151
http://www.hydroqual.com/GIS/GIS.htm

Gary Ostroff, P.E.
Co-Director
CommunityCartography
The Spatial Data Warehouse for the NYC Area!
http://www.ComCarto.com
1.877.MakeMap