VBA code to copy data to another sheet based on date range

See if this gets you started.

    Dim d As Date
    Dim m As String
    Dim w As Worksheet
     ' D2 is the cell in which you enter the date
    d = Range("D2").Value
    ' Get the full name of the month
    m = MonthName(d)
    ' Refer to the worksheet for that month
    Set w= Worksheets(m)
    ' Copy data to w below
    ...