As @TomBowen suggested, text files should not be used for this purpose. However, for learning purposes, we can oversee that.
I would suggest caching the path to your shared file. Have a loop (preferably async) that would constantly check when the file is updated and save the modified date locally. Do this by checking the last time the file was modified (How do I get modified date from file in C# on Windows Mobile?). If the modification date does not match your saved one - clear the console, read all the text file's content and print it to the console.
This would be a very primitive approach with tons of possibilities for stuff to fail. But it would work just for the sake of making something.