The following code will copy the data from the active workbook (columns A:D minus the header row). Then a closed workbook of your choosing will be opened. Copied data will be pasted in the first available row. Workbook will be closed and changes will be saved.
Dim lRow As Integer
lRow = Range("A1").End(xlDown).Row
Range("A2:D" & lRow).Copy
Workbooks.Open "C:\MyFiles\Test.xls" 'Change file path to match yours
Range("A" & Rows.Count).End(xlUp).Offset(1, 0).PasteSpecial
Application.CutCopyMode = False