In the MouseMove event handler, verify that m_Drawing is True. If it is, draw a line from the previously saved point to the current point. Then save the new current point.

In the MouseUp event handler, set m_Drawing to False.

Private m_Drawing As Boolean
Private m_LastX As Integer
Private m_LastY As Integer

' Start scribbling.
Private Sub Form1_MouseDown(ByVal sender As Object, ByVal e _
    As System.Windows.Forms.MouseEventArgs) Handles _
    MyBase.MouseDown
    m_Drawing = True
    m_LastX = e.X
    m_LastY = e.Y
End Sub

' Continue scribbling.
Private Sub Form1_MouseMove(ByVal sender As Object, ByVal e _
    As System.Windows.Forms.MouseEventArgs) Handles _
    MyBase.MouseMove
    If m_Drawing Then
        Me.CreateGraphics().DrawLine(Pens.Black, m_LastX, _
            m_LastY, e.X, e.Y)
        m_LastX = e.X
        m_LastY = e.Y
    End If
End Sub

' Stop scribbling.
Private Sub Form1_MouseUp(ByVal sender As Object, ByVal e _
    As System.Windows.Forms.MouseEventArgs) Handles _
    MyBase.MouseUp
    m_Drawing = False
End Sub