Since our team was working on SharePoint and SharePoint Online (an Office 365 service) for the last two years, and with the introduction of Windows 8 (with its new Windows runtime that can be accessed from native applications, JS/HTML applications and C#/XAML applications), developers can now harness the richness of the Windows 8 platform with the power of the cloud based Office 365 services and create innovative experiences. Although connecting the Office 365 service to Windows 8 applications is powerful, its not trivial to understand how to connect the two specifically since the platform authentication systems are not automatically connected.

My colleague Omar, wanted to help you overcome this initial hurdle and posted a great blog post to help you get started: http://blogs.msdn.com/b/omarv/archive/2012/10/25/windows-8-store-apps-office-365-enterprise-preview-sharepoint-online.aspx

UPDATE:

Many people responded and provided feedback to Omar on his blog and asked to also enable single sign on scenarios (not only using a vanilla Office 365 identity). Using single sign on federates an organization active directory with the Office 365 loud using ADFS and requires an additional roundtrip to the Office 365 STS to direct the authentication process. Omar updated the blog with a version 2 that support the federated identity scenario: http://blogs.msdn.com/b/omarv/archive/2012/11/15/developing-windows-store-apps-for-sharepoint-online-with-sso-single-sign-on.aspx.

Barak