This may help you get going.
Dim Date1 As String
Dim Date2 As String
Date1 = ">=" & Range("C1").Value
Date2 = "<=" & Range("D1").Value
Range("A:A").Select 'Assuming column A stores your dates
Selection.AutoFilter Field:=1, Criteria1:=Date1, Operator:=xlAnd _
, Criteria2:=Date2