The city of Hoi An has no airport, and no train station either. The only way to get here is by road. You can hire a taxi from the neighboring city of Da Nang. This town does have an International Airport, with daily flights to and from Hanoi, Saigon, and other Vietnamese cities. Da Nang also has a train station, with trains to and from Hanoi (12- 22 hr), Saigon (17-22 hr) and Hue (3 hr). You can also get to Hoi An from Da Nang on a bus.
If you want to visit Hue, you can get there in three hours on a bus. Form more information on Hue, visit the Hue on line Presentation.