You need access to the Xbox Live API, I think you have to apply to Microsoft to get on their 'Community Developer' programme, although it's a bit hazy on the site as to whether they are accepting applications or not.
One kind fellow (who I think is a Microsoft employee) saw that this was a terrible oversight from his employers decided to offer as web service that plugged into the Xbox Live network so you can pull statistics down, you can find info about it and a website here: -
http://duncanmackenzie.net/Blog/put-up-a-rest-api-for-xbox-gamertag-data
It's very comprehensive and should give you all the data you need (Gamerscore, current status, last game played etc)
EDIT: Extra stuff that might help
I'm not too familiar with C# but the process of using the service would be to do the following in your application: -
- Construct your URL with a/your gamertag as the argument
- Use some URL/Networking API (C#/.NET must have something like this somewhere) to load the URL and retrieve the contents. This should return you a big string containing a bunch of XML
- Parse the XML into your application using some sort of XML parsing API (again, I'd imagine C#/.NET has these things built into the framework)