There are a couple ways to request an application. First is to Click the 'Request an app" Link on the Home Page. This will send an email to the Okta admin. The user will have to specify the app they are requesting.
Another way is for the user to add an app. If the app is not listed, the user will need to create a bookmark. The bookmark requires the sign in URL and App name. There is an option to request the Okta admin to add this app. An email will be generated with the information the user provided.
Let me know if these two scenarios cover your use case or if you have any other questions.