The method given by the author is “overeating” in the article "Easiest way to throw up". That means you should eat more than your stomach can contain. Because once your stomach is too full to work regularly, it will automatically pull out the excessive load of food. This will result in your vomiting. But you should keep in mind that “overeating” only works in case of vegetables and healthy foods.
I have practiced this method for some times and I find it quite safe and easy to do. Just follow me and you will see the incredible result ;)
P/S: Just kidding. Do not use this way to lose weight. I think this will be harmful to you. If you want lose weight or lose fat but always be healthy, you should keep training everyday and apply a reasonable diet.