As many developers, I was also very happy to get to know, that Microsoft published a new REST API for Visual Studio Online. A feature of my main interest was the possibility to update a work item. On this site you can find a reference with some examples, how to use the REST API for updating a work item field.
According to the description, you just need to change a work item field, you’d like to update and pass it in JSON string with your HTTP-Request. Unfortunately, the world is not as simple as one would expect, and updating a work item state may get a little bit tougher in some cases. I have investigated the issue and collected all my knowledge in this blog entry. I know, this is a common problem and bunch of people out there are struggling with it at the moment. I hope, this blog entry can be helpful for them in some way.