Genuine means that something is sincere, honest, or true to its nature. It implies that there is no deceit or falseness involved. For example, you might say that a person is a "genuine friend" or that a piece of jewelry is a "genuine diamond."
Authentic means that something is real or original, and not a copy or imitation. It implies that something has a clear and indisputable origin or identity. For example, you might say that a painting is an "authentic Van Gogh" or that a person is an "authentic American."
Real means that something exists or is true, and not imaginary or false. It implies that something has a physical or tangible existence. For example, you might say that a person is a "real human" or that a problem is a "real concern."