If you want to build a client application for SharePoint Online such as a Windows 8 Metro App or a Windows Phone 7 app you will need to understand how active authentication works in Office 365 – a great background article on this is How to do active authentication to Office 365 and SharePoint Online which has a code sample listed below the blog post. This code sample uses the Microsoft.IdentityModel.dll which is part of Windows Identity Foundation and which you can normally find underneath - <drive>:\Program Files\Reference Assemblies\Microsoft\Windows Identity Foundation\v3.5\Microsoft.IdentityModel.dll
But since there is no version of Windows Identify Foundation available for the Windows Phone platform so you will need to create the SAML sign-in request programmatically if you want to build a Windows Phone 7 client for SharePoint Online. You can start by taking a look at the code sample Claims-SPOnline from Edin Kapic which does exactly that in a scenario with Windows 8. Unfortunately the code will become quite a lot more complex once you try to port it over to Windows Phone 7 since you can’t use the new async/await keywords which were introduced with .NET 4.5.
So if anyone has written a generic framework for authenticating against SharePoint Online from a Windows Phone 7.x – please leave a comment.