You handle the KeyPress event of the textbox, and test if e.KeyChar = Chr(13) then set e.Handled = True and select the next control in tab order.
Something like this:
Code:
Private Sub TextBox1_KeyPress(ByVal sender As Object, ByVal e As System.Windows.Forms.KeyPressEventArgs) Handles TextBox1.KeyPress
        If e.KeyChar = Chr(13) Then
            e.Handled = True 'This prevents the beep to sound
            Me.SelectNextControl(CType(sender, Control), True, True, True, True)
        End If
    End Sub
Edit: Bmahler beats me again