Boothbay Harbor has no rail or bus service. A car is effectively required. From Portland, take I-295 north to Brunswick, then US-1 north to the Boothbay Harbor exit (Route 27 south). The drive takes about 90 minutes. From Boston it's roughly three hours.
The nearest major airport is Portland International Jetport, with connections to most US hub airports. Bangor International Airport is another option if you're approaching from the north.
Parking in Boothbay Harbor is tight in peak summer season. The town operates a public parking area off Route 27 at the edge of town, with a short walk into the village centre.