If I want to read a local file from my project, given a relative path from the project directory, how could I achieve this?
You can get the ApplicationBasePath from PlatformServices.ApplicationEnvironment. This will make it possible to resolve non-absolute paths relative to your application base path.
Now that .NET Core has RTM-ed, you need to use IHostingEnvironment instead. It exposes WebRootPathand ContentRootPath.