Whether an image is the god, contains the god, or represents the god is a question Hindu theology answers in several incompatible ways, and outsiders have consistently reported only the crudest of them.
The ritual answer is that a properly consecrated image is inhabited. Consecration involves a rite of installing life-breath, and there are corresponding procedures for asking the deity to depart when an image is damaged or when a temporary image is to be dissolved, which is why the clay figures made for festivals are immersed in rivers and the sea at the end without any impiety. An image that has not been consecrated is not treated as anything in particular, and this is the detail that most often surprises people.
The philosophical answer, in the non-dual traditions, is that the absolute has no form at all, that images are concessions to human limitation, useful for concentrating an untrained mind, and are to be dispensed with eventually.
The devotional answer, in the bhakti traditions, is that the form is a real self-limitation undertaken by God for the sake of being loved, and that treating it as a mere aid is itself the error.
These three have coexisted for a very long time, and practitioners frequently hold more than one at once without any sense of contradiction. Accusations of idolatry, made by Muslim and Christian critics over many centuries and used to justify a great deal of temple destruction, engage only the first answer and only in its simplest form. It is worth adding that the critique is not solely external: Hindu reform movements of the nineteenth century, the Arya Samaj most sharply, attacked image worship from within on grounds that would be recognisable to any Protestant iconoclast.