That depends on you.
All Demigods are wired to read/understand Greek. So they have "Dyslexia" when it comes to English. Certain kids, like Athena's overcome it easily when they are young.
For most of their early lives, children go to school and everything. At around age 12 and up, as they begin to mature, their begin to "smell" godly. A scent that attracts monsters. Satyrs (protectors) are tasked with finding them and taking them to camp. Some children are never found until it is too late and they are killed.
(The life of a demigod is cruelly short, very few make it past thirty)
As I mentioned, some are not found or in an area that no monsters live in, so they can go on living but ALL demigods feel a calling for something else, a life of adventure or a life of whatever it is your godly parent is.
Example- Sons of Hephaestus love to work on cars. So tend to want to be mechanics or engineers/builders.
Children of Aphrodite love fashion or interior design.
Children of Apollo are beachhead/surfer types, love sunbathing and ranged sports.
Some parents are aware of their godly children and arrange to take their kids to camp half blood at a certain age, others prefer to hold onto them no matter the cost for whatever reason. It puts the child and parent in danger, or it can also damage the child, holding them back.
You can play your character how ever you wish, with no knowledge of Greek gods and such. But at some point, (unless the character is really weak) monsters will catch their scent and start to hunt them.
I hope that helps.
Also not all kids are "claimed" when they arrive at the camp. They might have a vision, parent tells them or a satyr finds them and takes them to camp.
Gods claim their children when the child "prove" themselves to their parent. Many kids go unclaimed for years and years.
In the books- Percy saw this and was mad at the gods for letting their children go unclaimed and he demanded they take more responsibility with their children. At least revealing who their parent is so they can move in with their halfblood siblings.