has daily flights from Lae as well as Port Moresby and also connects Alotau twice-weekly with the Trobriand Islands and with Misima. (http://www.apng.com/)
By ship
By coastal freighter.
It may be possible to reach Alotau from Port Moresby or Lae by cargo freighter. There is no passenger-only shipping. Ask around at Port Moresby or Lae harbors, and be prepared for a long wait!