Why do you want to throw up? Answering this question will help to determine the best method.

Here are some common scenarios:

If it's something like getting out of a test or school then all you need to do is make throwing up SOUNDS in the toilets until a teacher comes then flush the toilet, and rinse your mouth with soda and come out carrying the soda and looking miserable. They'll assume you threw up and that'll be it.

If it's to purge after eating large amounts in a binge-eating disorder then don't. A better solution to wanting to feel "full" is to drink lots of green tea, and then eat a moderate amount. The green tea will help to block fat absorbtion, preventing weight gain, and the liquid will help you to feel "full". Also, seek professional help.

If you want to throw up because you believe you've ingested a poison, then don't. When you vomit you're sending all the stomach acid up through your throat. While bile does help to neutralise some of the acid there will still be burns, and the poison has multiple entry points into your blood stream. Throwing up poison effectively more than doubles the chance of it entering your blood stream and doing damage. Ironically in many cases just leaving the poison in your stomach acid will neutralise it (stomach acid is pretty strong stuff). Rather get to a hospital, let medical professional decide the best course of action depending on the poison involved.

If you want to throw up on someone in a fight to deter them then... okay, weird, but not really much weirder than the "shit in your hand and throw it" technique mastered by monkey ninjas around the world. The gag reflex normally does it. By sticking your fingers down your throat you can normally induce vomiting. The problem here is that if you do this repeatedly you almost always leave marks on your hand (either from biting down or exposure to vomit) that medical personnel will automatically recognise as "Russell's sign", as will many teachers, school guidance counsellors, and lots of other people who know what to look for. The bottom line is that if you do this often people will know.

If you lack a gag reflex? Well, you may lose your fight, but you'll have a fine career ahead of you in porn, so you'll have enough money to hire someone to kick those people's asses for you.