How to implement remember me fucntionality in Windows application

Easiest way is to add a field to your Settings.settings file.
Double click on "my Project" in teh Solution Explorer, and select the "Settings" tab on the left.
Add a setting:

Name = UserName
Type = String
Scope = User
Value = (leave blank)

Then in your code:

Dim userName As String = My.Settings.UserName
If (Not String.IsNullOrWhiteSpace(userName)) Then
    ' use user name
End If

To save it again:

My.Settings.UserName = userName
My.Settings.Save()