By air: the closest airports are at Baia Mare (about 70 km south, 90 minutes by car) and Cluj-Napoca (about 220 km, four hours by car). Cluj has more international connections; Baia Mare has cheaper flights from Bucharest.
By train: Sighet has rail connections to Vișeu de Jos (and from there to Cluj and beyond), but the journeys are long and slow. The night train from Bucharest is the romantic option (around 14 hours).
By car: the most flexible way to arrive. From Cluj-Napoca, the DN17 climbs over the Prislop Pass — a beautiful but slow drive through the Rodna Mountains. From Baia Mare, the DN18 climbs through the Gutâi Pass. From Maramureș you simply continue east.
Border crossing: there is a road crossing into Ukraine at Sighet — across the Tisa River into Solotvyno — but the political situation has often complicated this.