How do I prevent a form from being resized by the user?

To prevent users from resizing, set the FormBoderStyle to Fixed3D or FixedDialog from properties window or from code

frmYour.BorderStyle = System.WinForms.FormBorderStyle.Fixed3D

And set the WindowState property to Maximized, set the MaximizeBox and MinimizeBox properties to false.

To prevent the user from moving around, override WndProc

Protected Overrides Sub WndProc(ByRef m As Message)
        Const WM_NCLBUTTONDOWN As Integer = 161
        Const WM_SYSCOMMAND As Integer = 274
        Const HTCAPTION As Integer = 2
        Const SC_MOVE As Integer = 61456

        If (m.Msg = WM_SYSCOMMAND) And (m.WParam.ToInt32() = SC_MOVE) Then
            Return
        End If

        If (m.Msg = WM_NCLBUTTONDOWN) And (m.WParam.ToInt32() = HTCAPTION) Then
            Return
        End If

        MyBase.WndProc(m)
    End Sub

//Set fixed border
yourForm.FormBorderStyle = System.Windows.Forms.FormBorderStyle.Fixed3D

//Set the state of your form to maximized       
yourForm.WindowState = FormWindowState.Maximized

//Disable the minimize box and the maximize box
yourForm.MinimizeBox = False
yourForm.MaximizeBox = False

Set the highlighted properties. Set MaximimSize and MinimizeSize properties the same size