Authenticate Users Against My WordPress User Group

I am building a mobile app for Windows Phone 7 and it is an extension of my wordpress site, so I would like to have users that login/register on my app to be able to use their user account from my wordpress site or create a user account on my wordpress site if they are registering.

There is an official wordpress app for Windows Phone which allows you to login to your wordpress site so I know it is possible to validate a user via a smartphone application. I guess my question is more about how I would need to go about doing that.

This is the first app that I am writing that uses authentication so I am a total noob about this stuff.

Thanks in advance for your help.