1.
Response.Cookies("userName").Value = "Spider_User"
Response.Cookies("userName").Expires = DateTime.Now.AddDays(2)

2.
 Create user id and password cookies
    Dim cookie_test As HttpCookie = New HttpCookie("Userid")
    cookie_test.Value = "Spider_user"
    cookie_test.Expires = #30/03/2004#
    Response.Cookies.Add(cookie)
    cookie_test = New HttpCookie("Pwd")
    cookie_test.Value = "test"
    cookie_test.Expires = #30/03/2004#
 Response.Cookies.Add(cookie)

Dim cookieCtrls As New HttpCookieCollection()
cookieCtrls = Request.Cookies

Dim str As String
For Each str In cookieCtrls
   ListBox1.Items.Add("Cookie: " + str)
   ListBox1.Items.Add("Value:" & _
     Request.Cookies(str).Value)
Next 

Request.Cookies.Remove("Pwd")
Request.Cookies.Remove("Userid")

(or)

We can set date -1 value as the cookie expires date for removing the cookie

Dim i As Integer
Dim cookieName As String
Dim limit As Integer = Request.Cookies.Count - 1
For i = 0 To limit
   aCookie = Request.Cookies(i)
   aCookie.Expires = DateTime.Now.AddDays(-1)
   Response.Cookies.Add(aCookie)
Next

Response.Cookies("user")("Name") = "mike"
Response.Cookies("user")("ModifiedDt") = DateTime.Now.ToString
Response.Cookies("user").Expires = DateTime.Now.AddDays(2)

Dim appCookie As New HttpCookie("testAppCookie")
testAppCookie.Value = "written " & Now.ToString
testAppCookie.Expires = Now.AddDays(1)
testAppCookie.Path = "/Applicationpath"
Response.Cookies.Add(testAppCookie)