How do reach ajanta and ellora?

They are both caves in Maharashtra State in India.

The Ajanta caves are cut into a granite cliff in the Wagurna river valley 8 kilometres from the village of Ajanta.The 29 caves are a Buddhist sanctuary and contain magnificent sculptures and murals.The Ellora Caves are 25 kilometres northwest of Aurangabad. Their eastern group comprises 12 Buddhas, 17 Brahmin and 5 Jain works.

Further to above answer I forgot to mention that you can get flights to Aurangabad Airport from New Delhi or Mumbai. from where there is public transport to both the Ajanta Caves and Ellora Caves. There is also a railway station at Aurangabad. The Ellora caves can also be reached by train to Jalgaon railway station, and there are good road to Aurangabad and Jalgaon from other parts of India and coach tours are available for visitors to get there from Indian cities.