Hinduism believes, there is God in both living (animate) and inanimate things. The saying goes 'kan kan me Bhagwan hai' or God lives in every atom. Therefore, many inanimate things are taken together and used to represent God. Even drawings symbolize the almighty.
Ganesh is the 'pratham pujya' or worshiped first, in every thing. So Ganesh is needed every where. How then do we make Ganesh??
Paint a Swastic symbol and put some rice grains on it...its Ganesh. The symbol of OM in Hindi represents Ganesh. Wrapping a thread around a piece of clay is Ganesh. Take a piece of cow-dung and wrap a thread around that and you have Ganesh. A betel nut (supari) or a piece of turmeric (haldi), wrapped with a thread is Ganesh.Ganesh exists in a dot made with roli.Two pieces of 'dubh' grass wrapped with thread is also Ganesh.
Ganesh is the 'Shubh karta' or one who makes auspicious and 'Vighna harta' or one who gets rid of obstacles.