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.
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How to Reach Sukhothai from India
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.
How to reach Sukhothai by flight
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.
How to reach Sukhothai by road
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.
How to reach Sukhothai by train
You can take an express train from Bangkok or Chiang Mai to Phitsanulok which takes 7 hours, and then take a bus to Sukhothai.
How to reach Sukhothai by bus
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.
Local transport in Sukhothai
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.