International Airports:
Helsinki-Vantaa Airport (for example Finnair)
Tampere Airport (for example Ryanair)
By train you can travel all the way from Helsinki to Savonlinna, and from there by bus to Sulkava. The Savonlinna trainstation is closed, you need to buy ticket directly from the train when departing from Savonlinna.
Timetables: www.vr.fi/eng
By bus to Sulkava center.
Timetables: www.matkahuolto.fi/en/ .
By flying less than an hour from Helsinki by Finncomm Airlines to the cities of Savonlinna and Varkaus, rest of the trip to Sulkava by bus.
Timetables: www.fc.fi/home.html .
By car the trip from Helsinki to Sulkava lasts about 4-5 hours.
Also bus timetables for other cities from Sulkava: www.matkahuolto.fi/en/