Real Tonga flies to Ha'apai from Tongatapu daily except Sunday, and from Ha'apai to Vava'u three or four times a week. Pilolevu Airport (HPA) is at Koulo, five km north of Pangai.
Some of the places to stay offer free transfers, otherwise a taxi is usually available. (The main road to the north end of Lifuka crosses the airstrip and a gate must be closed during flight arrivals.)
Ferries between Nuku'alofa and Vava'u call regularly at Pangai, northbound early Tuesday morning, southbound on Wednesday night. Ships tie up to Taufa'ahau Wharf near the center of Pangai.
There's a large passenger shelter on the wharf where you can wait until dawn if you happen to arrive in the middle of the night (as is sometimes the case).
When there are strong westerly winds, the ships may not risk landing at Pangai.