There are air-con busses leaving from Mo Chit Northern Bus Terminal in Bangkok every 30 minutes, daily from 7 am to 11pm.You can to get to the bus terminal, take the MRT underground to Kamphaeng Phet Station and from there a motorbike taxi (30 baht) to Mo Chit Bus Terminal.
Once you arrive at the Sukhothai Bus Terminal (see picture below) there are songthaews (shared pick-up taxis) taking you to the foreign hotel area in New Sukhothai which is located about 2,5 km drive from the bus station. One way fare: 50 baht. They also drop you off right at the door of your hotel if you ask them to with no additional charge.
There is no train station in Sukhothai. If you still want to take the train as close to Sukhothai as you can, I recommend traveling to Phitsanulok (5 hours) and take the bus from there to Sukhothai (1 hour)
Sukhothai airport is located about 40 km north of New Sukhothai. There is only one airline which owns the airport and has two daily flights to and from Bangkok: Bangkok Airways. The one way fare is from 2,000 baht and the flight takes about 70 minutes. Once reached the beautiful tropical architecture designed small airport, Bangkok Airways offers transport to New Sukhothai, 30 mins, 120 baht one way.