You can be claimed in a few ways. And no, not everything is like the PJO books. You can be claimed with a dramatic glowing symbol over your head, or you could be claimed through dreams, visions, or prayer.
Praying to the Gods is one way to be claimed. Call upon the major gods first, and don't forget the minor gods such as Nemesis. The claiming process takes a while. It took me around a year before I got stone hard evidence that I was a child of Athena.
Don't be discouraged! It'll happen in time. The gods have reason to claim you when they do. Don't give up, it'll happen if you're a true demigod.
Meditation also works. It may seem very 'guru-Hindu,' but it truly works. Just make sure you're in a quiet place with no interupption.
Sometimes dreams or visions can dictate that you've been claimed. For me, I had a dream (shush, no, not Mr. Luther King Jr.,) that included an olive tree and an owl. With my personality it made sense: I was claimed by Athena.
Best of luck, demigods!