Hi,
Web apps are accessed from your SharePoint site.
If you open your SharePoint site and navigate to a document library, you can add a new document by navigating to the top panel, hit Documents and select New Document. You will then be able to create a document corresponding to the file template of that library. (Explained in detail in the links I provide below)
Please see the following links to get started:
office.microsoft.com/.../start-using-office-web-apps-in-sharepoint-HA010380116.aspx
office.microsoft.com/.../get-started-with-office-web-apps-in-office-365-HA102619009.aspx
office.microsoft.com/.../set-a-file-template-for-a-document-or-form-library-HA010377912.aspx
If you still can't find the functionality; To use web apps, your Office 365 user needs to be enabled for Web Apps, which it should be if it is assigned the full E2 license. Please verify that your user account is assigned a Web Apps license (or "full E2").
What do you mean by "Home screen"? If you mean that your users have Icons to Office applications on their desktop, Start menu or Windows 8 home screen, that is because they have Office installed on their computer. The Icons opens their locally installed version of Office, from where they can save documents to your Sharepoint site.
Hope this helps,
Jesper Ståhle