This will work for a basic one. Thats assuming that the file will always be in the same location.
Code:
Public Class Form1
Private Sub Form1_FormClosing(ByVal sender As Object, ByVal e As System.Windows.Forms.FormClosingEventArgs) Handles Me.FormClosing
My.Computer.FileSystem.WriteAllText("C:\TextBox.txt", TextNote.Text, False)
End Sub
Private Sub Form1_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load
TextNote.Text = My.Computer.FileSystem.ReadAllText("C:\TextBox.txt")
End Sub
End Class