I am new to asynchronous programming with the async modifier. I am trying to figure out how to make sure that my Main method of a console applicati         
        
You can solve this with this simple construct:
class Program
{
    static void Main(string[] args)
    {
        Task.Run(async () =>
        {
            // Do any async anything you need here without worry
        }).GetAwaiter().GetResult();
    }
}
That will put everything you do out on the ThreadPool where you'd want it (so other Tasks you start/await don't attempt to rejoin a Thread they shouldn't), and wait until everything's done before closing the Console app. No need for special loops or outside libs.
Edit: Incorporate Andrew's solution for uncaught Exceptions.