With the grateful help of witek I got this to work. This is what I did:

(1) Using Visual Studio Express 2010, I created a project called squareDLL consisting of:

square.c:

double _stdcall square (double x)
{
return x * x;
}

square.def:

LIBRARY "square"
EXPORTS
square

and stored it at this location:

C:\Users\Owner\Documents\Visual Studio 2010\Projects\squareDLL\Debug\squareDLL.dll

(2) In Excel I setup:

Private Sub Workbook_Open()

Dim sParm As String, sDQ As String

sDQ = Chr(34) 'Double quotes

sParm = ""
sParm = sParm & sDQ & "C:\Users\Owner\Documents\Visual Studio 2010\Projects\squareDLL\Debug\squareDLL.dll" & sDQ & ","
sParm = sParm & sDQ & "square" & sDQ & ","
sParm = sParm & sDQ & "BB" & sDQ & ","
sParm = sParm & sDQ & "square" & sDQ & ",,1"

Application.ExecuteExcel4Macro ("REGISTER(" & sParm & ")")

End Sub

(3) I was then able to use the square function, in a cell in my worksheet, like this:

=square(C2)
=square(45)