Air
Aurangabad is the closest domestic airport - just 30 kms away.
Rail
Aurangabad is well connected by rail to the rest of the country. Though if you are coming in from Delhi or Mumbai, it may be better to take the rail connection to Jalgaon which is 59 kms away from Ellora. Regular bus service and taxis are available to Ellora from here.
Bus
State transport buses connect the whole of Maharashtra. You could also drive in from Pune or Mumbai