Remember those old cartoons where someone would grab a loose thread on a sweater and the whole thing would fall apart? Well, it will happen to your fly if your finishing isn't up to par.
The most common and very secure finish is the whip finish. A whip finish can be performed by hand, or with an assisting tool.
In my opinion the Matarelli whip finish tool is the best one out there. It is usually the most expensive, but well worth it.