You can do that without having to write any code.
Select a control on your form (or with nothing selected to create a setting for the form itself), and in the Properties tool window, expand the first item (ApplicationSettings). Then select (PropertyBindings), and click the button to the right. In the dialog, enter a name for the setting, and the value.
In the case of a standalone executable, you're done. In the case of a form used in AutoCAD, you have to manually save the settings when the form is closing, which you can do using the Properties.Settings class created by the designer:
Properties.Settings.Default.Save();
The Settings class can also be manipulated manually, or modified to have additional settings that don't correspond to a Component. You'll find it in the Properties node of your project in Solution Explorer.