How do I find shaded text in a large document?

Edit them how?
The following macro will locate all cells with the same background shade as the selected cell and write some text (highlighted) into the cell (so don't test it on your original document!!!!)

Sub Macro1()
Dim oTable As Table
Dim oCell As Cell
Dim iCol As Long
    If Selection.Information(wdWithInTable) = True Then
        If MsgBox("Is the selected cell the required shade?", vbYesNo) = vbYes Then
            iCol = Selection.Cells(1).Shading.BackgroundPatternColorIndex
            For Each oTable In ActiveDocument.Tables
                For Each oCell In oTable.Range.Cells
                    If oCell.Shading.BackgroundPatternColorIndex = iCol Then
                        'Do what you want with the cell here e.g
                        oCell.Range.Text = "This cell has shading!"
                    End If
                Next oCell
            Next oTable
        End If
    Else
        MsgBox "Put the cursor in a cell of the colour you wish to process and run the macro again"
    End If
End Sub

Er, um, well, thank you for all your work, but this is WAY beyond my technical ability.  All I know about macros is that they are a series of repeated actions.  What I was looking for was some way to search for cells of a particular color, so I could see what was in them, in the same way a search can be done for highlighted text.

What you require is not available. The macro will do what you need and is quite simple to employ - see http://www.gmayor.com/installing_macro.htm  

Put the cursor in a table cell of the required colour shading and run the macro. It will locate each cell from that point in turn and select it so that you can see the content, and then gives you the options to stop or continue to the next. When you wish to resume, leave the cursor in the cell you have stopped at and run the macro again. It will continue from that point.

I have modified it slightly so that you can do almost what you wish (see below).

Sub FindCellColor()
Dim oRng As Range
Dim oTable As Table
Dim oCell As Cell
Dim iCol As Long
    If Selection.Information(wdWithInTable) = True Then
        If MsgBox("Is the selected cell the required shade?", vbYesNo) = vbYes Then
            iCol = Selection.Cells(1).Shading.BackgroundPatternColorIndex
            Set oRng = Selection.Range
            oRng.End = ActiveDocument.Range.End
            For Each oTable In oRng.Tables
                For Each oCell In oTable.Range.Cells
                    If oCell.Shading.BackgroundPatternColorIndex = iCol Then
                        oCell.Select
                        If MsgBox("Edit this cell?", vbYesNo) = vbYes Then Exit Sub
                    End If
                Next oCell
            Next oTable
        End If
    Else
        MsgBox "Put the cursor in a cell of the colour you wish to process and run the macro again"
    End If
End Sub