In our Hinduism, we have large number of gods and goddesses, who are worshipped as deities. The Deities appearances would differ from each other. The first god Lord Vinayaka, looks half human, and half elephant. Similarly the avatars of Lord Vishnu are also looks differently. Lord Narasimha appears in the form of half lion and half human and Lord Varaha, Lord Hayagriva, Lord Kurma and Lord Matsya are also appear in the form of half human and half animal.
The great Garuda Bhagavan is the Vahana of Lord Vishnu, and he is displayed in the pictures in the form of half bird and half human. Similarly Nandi Bhagavan also appears in the form of a bull, and he eagerly watches his master Lord Shiva, without wasting even a second. All these divine messengers contain great knowledge and wisdom, and they are having the powers equivalent to their masters.
Actually, most of the Hindus are not having the adequate knowledge about our deities, and about the avatars taken by them. Similar to the Holy Christians and the Holy Muslims, Hindus are not that much interested in verifying the Puranas and other Holy texts. They are considering all these things only as stories, and are not deeply involving into that. They have to clarify their doubts with the Vedic pundits and with the Pontiffs of the Holy Mutts.
Some Hindus are even commenting on the appearance of the gods and goddesses, like Vinayaka and Varahi Amman, and they are considering them simply as dolls. Before installing all the divine deities in the temple, proper puja would be performed, Mantras would be chanted and after the performance of the Homams and the Vedic rituals, the divine idols would get sufficient powers, and the gods and the goddesses would permanently dwell into that.
Lord Vinayaka is our first god, and he is the one who removes the obstacles in our life, and would give all kinds of prosperity in our life. By seeing the idol of Lord Vinayaka, we must have to get sincere bhakti on him, and must adorn him with flowers, flower garlands, and must offer fruits and Modakams as Holy Prasad to him.