I always tell my patients that the first useful thing to do is place the burn under cold water for several minutes. This limits its expansion and soothes the pain. The burn's depth then needs to be assessed in order for it to be treated appropriately. Boiling water produces very painful burns, but they are often not as deep as those caused by boiling oil, which can reach the deep dermis. If the burn is deep, they must cover it with sterile wound care gauze and consult their doctor.
When the skin is red, and only the epidermis is affected (like after sunburn). This will encourage the epidermis to rebuild itself and soothe the pain. It is also essential to protect the burn to avoid contact with irritant products and to prevent any secondary infection.
... and needs to be protected. There are specially designed dermo-cosmetics for this. If the mark left by a burn remains red, gets thicker and itches, it is best to get it checked out. Especially since cheloid scarring can occur, which is unsightly and causes itching. These scars require specific treatment. The scar must also be protected from the sun with a high factor sunscreen.