Is you environment in Azure? You could spin up one of the default Linux VMs, Install Nginx (http://wiki.nginx.org/Main) and run Node on there. I would also look into Cloud 8 IDE (https://c9.io/)
I started looking at Node about a year ago...and I know this doesn't answer your question directly, but you are asking (intro/basic) simple questions..I would pick up: Node.js In Action (http://www.manning.com/cantelon/), which includes very good tutorials and deep level intro into Node.js
To answer you question you asked about interacting ASP.NET with Node.js, absolutely it can work on several levels. You can have a Node.js server implemented using RESTful services, POX Services, Socket.io/WebSockets and they can interact with ASP.NET on the server side and/or use Ajax calls from your client to the Node.js endpoints.
That is actually the preferred way of implementing a complex/enterrpise application since Node.js is great for non-blocking I/O...however it is not great a synchronous tasks (complex CPU intensive tasks). Therefore, you can have your Node.js services do your: data retrieval/CRUD operations and ASP.NET handle the Business Logic (i.e. any complex math, physics, LINQ, concurrency tasks etc.)