I have code and it somewhat works. It does copy a worksheet from a workbook in a array of workbooks and then pastes the data to a master Workbook/Worksheet correctly. When it copies and pastes the another sheet to that master workbook/worksheet, it does find the last row and pastes that correctly. However, when it goes to the next workbook and sheet in the array, it copies the sheet okay, but does not paste it starting at the last empty row. Yes, I know this is simple, but not getting there.
If IsArray(FileArray) Then
   For i = LBound(FileArray) To UBound(FileArray)
      Set myBook = Workbooks.Open(FileArray(i))
      Sheets("Sheet1").Select
      Rows("1:4").Select
      Selection.Delete Shift:=xlUp
      For Each mySheet In myBook.Worksheets         
        mySheet.Range("A1").CurrentRegion.Copy
        Basebook.Worksheets(1).Cells(Rows.Count, 1).End(xlUp).Offset(1, 
        0).PasteSpecial Paste:=xlPasteValues
      Next mySheet
      myBook.Close
   Next i
