You can get a flight which takes you directly to the airport in Puta Cana. If you land at Santo Domingo or La Romana, you can take a bus or mini-van to get to Punta Cana at effective costs.
Direct flights from India are not available to reach Punta Cana. You'll be required to change flights maybe more than twice to reach here.
Punta Cana International Airport is the most convenient airport to land at, from where you can reach the East coast resorts in 10 to 40 minutes. There are domestic flight services availed by Dominican Shuttles.
Cars and cabs are available for rent to traverse in and around Punta Cana. However these options might get heavy on your pocket.
Public buses are in abundance if you want to get to a nearby city.
Taxis and public buses are available to get around the east coast. Beach taxis can be used to commute on the beach to visit some of the hotels. There are also some mini-vans available for people using wheelchairs. You can also rent a car or scooter to travel around, but don't forget to get insured and check out the driving rules and laws followed there first.