The compound that makes hot peppers burn dissolves in oil, not water. That is why rinsing with water alone will not remove it from your hands; it stays on the skin and leaves a burning sensation that can last for hours. The right way to clean your hands is with soap, dish soap, or by rubbing them with oil first and then washing. The safest approach is to wear gloves and clean the knife and cutting board right away.
The heat from hot peppers comes from a compound that stimulates nerve endings, not from an injury. This compound sends a heat signal to the body; the skin is not actually burned, but the brain perceives it as burning. Its most important property is that it dissolves in oil and barely dissolves in water. This one property explains both why water does not remove it and why it lasts so long. Drinking water to reduce the heat does not work either; water only moves the compound around your mouth. The level of heat varies greatly by pepper variety, and not every pepper of the same variety is alike.
The delayed onset is surprising, too. While cutting peppers, you often feel nothing; the burning starts half an hour, sometimes an hour later, and gradually intensifies. In the meantime, your hands may have touched your face, eyes, or other areas. That is why precautions are taken before you feel anything: if you know you will be cutting hot peppers, put on gloves. Thin kitchen gloves or food-safe bags can be used as gloves. Applying something cold after the burning starts provides temporary relief but does not remove the compound from the skin.
If you do not have gloves, the cleaning method changes. First rub a little cooking oil over your hands; the oil absorbs the compound left on the skin. Then wash and rinse with plenty of lather from dish soap or hand soap. Running water alone does not work and may even spread the compound over a larger area of your hands. Milk, yogurt, or ayran can also soothe your hands within a few minutes. Pay particular attention around the nails and between the fingers, because that is where the compound remains most. If your hands have cuts or cracks, the effect is much more severe, so gloves become essential.
The most important rule is to keep your hands away from your eyes and face. Do not touch your face while cutting peppers or afterward, and do not rub an itchy eye. If pepper gets in your eye, remove contact lenses if you wear them, rinse the eye with plenty of lukewarm water for 15 minutes, and seek medical attention if the burning does not go away. Take the same care around children: work so little hands cannot touch the counter where hot peppers are being cut. The dust released when dried hot peppers are ground has the same effect and causes coughing when inhaled.
Tools and surfaces can transfer the compound, too. Residue on a knife, cutting board, or plate transfers to the next ingredient; if you chop cucumber right after hot peppers on the same board, the cucumber will be hot, too. So wash the board and knife with dish soap. Because most of the heat is concentrated in the seeds and white ribs, set those parts aside in a separate bowl. If you are going to keep chopped peppers, put them in a sealed container because peppers left uncovered spread their aroma. Wash the cloths and sponges you used separately, too, because the compound remains on them.