Demi-Gods in Rick Riordan's books are not your usual kids. Demi-Gods are kids who have one parent who is a god or goddess and other parent is a human. Their parents are well aware if their child is a Demi-God, and it is partly their job to protect them from monsters as they grow up.
Throughout a Demi-Gods childhood they will be followed by strange occurances, an example is seeing people who don't look human, maybe they have one eye, or look like a reptile. Since the Gods and Goddesses communicate mainly in Greek, Demi-Gods' brains are set to recognize the Greek alphabet and have trouble reading english, the doctor they go see will just say they are dyslexic. Doctors will also say they have ADHD, but really their bodies are just energized so they won't get tired in battle. Some Demi-Gods, Percy for example, will never stay in a school for a long amount of time, due to the strange occurances that follow them around like a shadow.
Once they around twelve more and more monsters will realize they are a Demi-God because that is around the time they are ready to start training and their parents tell them that they are a Demi-God. Even more monsters will come once the child recognizes the fact that one of their parents is a Greek God or Goddess.
Luckily, there is a place where Demi-Gods are well protected. Located in New York is Camp Half-Blood. Half-Blood is another name for Demi-God. When the Demi-God gets there, they will first be brought to Chiron and Mr. D (Dionysus) before seeing a video, we never find out what the video is because Percy didn't see it due to his Minotaur attack. Then if they know which God or Goddess is their parent they will be shown to the cabin dedicated to their parent. If they don't know who their parent is, they will stay in the Hermes cabin until their parent claims them by sending their symbol over the kids head. Once they decide to stop going to camp they will go live in the real world. Few demi-gods live through adulthood even after they've been trained.
Most of the heroes in Greek myths are considered to be Demi-Gods. Hercules was the most famous of them all. He was the son of Zeus and a mortal woman. Some well known people from history are considered to possibly be Demi-Gods, Alexander the Great is one of these people. Demi-Gods in myths only would be in grave danger of dieing if they were on a quest, or if they were considered a threat, for example, Hercules was Zeus' son so he was bound to be a great hero, so some people would want him dead so he wouldn't be a threat.