I wish to conditionally add an item to a menu. I have a custom module and a menu called "links". How would I add an item to a menu in my module code?
The menu system is cached, so you can't add or remove menu items as you please based on user, page viewed, custom logic etc. That is you can't do it without having to clear the menu cache which would cause a severe performance hit.
What you could do, to create this effect is to create some custom logic to define the access control on the menu item. Since Drupal hides menu items that users doesn't have access to, you could under certain circumstances deny permission to hide the menu item. This is a bit hackish solution.
Another solution which I would prefer, would be to use js or css to hide or show the menu. You could dynamically add/remove a class on the body to determine if the menu item should be shown or not. This would quickly become unmanagable if you need several of these kind of menu items, however.