Buddhist art & culture is a huge topic with an enormous range of material available for discussion. This site is predominantly Theravadin so discussion will be directed accordingly - with mandalas as one major exception. The main elements of Buddhist art are fairly universal and, as space permits, various expressions from all Buddhist lineages will be presented.
Although Buddhism began in the sixth century BCE the oldest surviving artefacts are relatively more recent - nothing in Buddhist archaeological record can be safely dated before the third century. The first independent evidence of Buddhism comes from the reign of the Mauryan Emperor Asoka (273 - 232 BCE) whose stone inscriptions are the earliest Indian historical records.
These inscriptions make reference to the dhamma, recommend certain texts, the Buddha's teaching in general and condemn schism. They record his visit to the Buddha's birth place (Lumbini), his restoration of the nearby stupa and indicate a visit to the Bodhi tree at Bodh Gaya, site of the Buddha's enlightenment.
Buddhism in India was at the height of its influence from 250 BCE to around 500 CE. During this time an enormous amount of functional and devotional material was produced and the energy of the Buddha's dispensation was changing the whole face of civilisation in Central Asia and beyond. It was able to gather into itself all the intellectual and artistic currents of the age, uniting ideas from as far as the Greco-Roman world of the West and China in the East.
Indian artists and builders have until modern times always been anonymous craftsmen and older works are never signed. The only record, if any, is of the sponsor who would usually be a member of the local nobility or merchant class although there are regular references to monks or nuns providing funds (presumably either money relinquished on ordination or passed on from lay supporters).
Although there were an enormous number of monasteries built around the time of the Buddha very little remains of these beyond the foundation stones. The style of these buildings would have been according to local traditions - perhaps incorporating some of the early aniconic symbols as decoration. Excavation of rock monasteries started on a large scale in the early 2nd century and provide a wealth of architecture, sculpture and paintings for study.
The earliest specifically Buddhist monument is the stupa and the development of much Buddhist art has been in relation to the decorative and architectural evolution of this form. The appearance of Buddha images was not until around the first century BCE and their function was originally similar to that of the stupa - relic containers in the first instance and then becoming 'reminding relics' in their own right.
The Buddha's teachings remained an oral tradition for several centuries after his death but gradually written scripture evolved into a significant art form providing not only textual information but artistic and symbolic inspiration.