You can take a flight from Bangkok to Sukhothai airport. Otherwise, better options are taking a train from either Bangkok or Chiang Mai to Phitsanulok and then bus to Sukhothai; or bus from Bangkok, Chiang Mai, Phitsanulok or Mae Sot.
Indians can take a flight from all thr major cities of Mumbai, Delhi, Banglore, Kolkata, Ahemdabad, etc to Suvarnabhumi airport of Bangkok. Then they can take a flight, train, bus or car whatever they desire, to Sukhothai. Popular airlines from India to Bangkok are AirAsia, Thai Airways, Indigo, Jet Airways, etc.
You can take a flight into Bangkok's Suvarnabhumi airport first, and then fly from Bangkok to Sukhothai's airport. It costs between 2,000-2.700 Baht.
You can make a car journey from Phitsanulok, Bangkok or Chiang Mai to Sukhothai, but these will cost you a lot, be extremely uncomfortable and waste a lot of time just in travelling.
You can take an express train from Bangkok or Chiang Mai to Phitsanulok which takes 7 hours, and then take a bus to Sukhothai.
Buses run freregularly from Mae Sot taking 3 hours, and from Phitsanulok taking 1 hour. Bus journeys from Bangkok and Chiang Mai are possible, but they are long taking 6-7 hours, and uncomfortable.
You can take conthaews to and from the bus station, running the Charodwithitong road for around 10-20 Baht. Tuk tuks are also available to go from New Sukhothai to Old Sukhothai in arrpoximately 400 Baht. Bicycle and motorbike rental services are also provided by some hotels and guesthouses.