Depends a lot on the reason for the nausea and vomiting. If it's an intelligent thing your body is doing (i.e. there is a good reason for expelling what's down there - food poisoning, drunkenness, mild travel sickness), encouraging the vomiting is the best way to go. Then it's all over as quickly as possible. If the nausea/vomiting has nothing to do with the food/drink in the stomach and it's definitely safe for the food/drink to stay where it is, then antacids for nausea and anti-vomiting pills in cases of mild vomiting is the way to go. If someone is in a bout of severe vomiting there's not much you can or even should do except watch the person and if it continues to the point of being dangerous (i.e. continuing even after lots and lots of dry retching and showing no signs of stopping) and then you just have to take them to the hospital.
If you know that it's going to happen and it's definitely goign to be safe for the food/drink to stay in the stomach, there are anti-nausea/vomiting pills you can get from your pharmacist.
If it's not safe for the food/drink to stay in the stomach and you repress the vomiting - like if you take anti-nausea pills before getting ridiculously drunk - then you could kill yourself by accident.
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