Best way to add custom controller?

Create custom module. Take any existing module as example. (for example aff) :
1. Create folder /amember/application/modulename
2. Create module.xml (contains module description) and db.xml if you require database modifications.
3. Create bootstrap.php that will contain Am_Module child:
class Bootstrap_Modulename extends Am_Module
and create handlers for hooks.
4. Then create:
/controllers/ - folder where you will store your custom controllers.
/library/ - folder where you can include your custom classes.
/views/ - folder where your custom views will be stored.