I'd never tried to do this until today, but it's actually very easy to do. In the example below, I am executing a command on the database inside of a Try/Catch block. In the case that the command fails, the catch block writes details of the exception to the Application Event Log.

Note that you can plug any string into the first parameter, I just have it set to provide the product name of the application (Application.ProductName) which is nicer than a static string for when you embed this code into a reusable class.

Try
  oCommand.ExecuteNonQuery()
Catch ex As Exception
  strStatus = "Error #" & Str(Err.Number) & " was generated by " & Err.Source & vbCrLf & _
  Err.Description & ". The error occurred in function makeConn."
  EventLog.WriteEntry(Application.ProductName, strStatus, EventLogEntryType.Error)
End Try