The ports include Madang, Lae, and Port Moresby on the mainland, Kieta on Bougainville, and Rabaul and Kimbe on New Britain. However, they are only internal ferries. International ferries are unavailable.
There are also cruises such as the Coral Princess and ones from Aurora Expeditions.
Few travellers travel between Buin in Bougainville and Shortland Island in the Solomon Islands by a banana boat. There are flights between Shortland Island and Gizo or Chiusel in the Solomon Islands (alternatively banana boats on very rough seas). This route has been described on a few blogs and older editions of the Lonely Planet.
The only land border is with Papua (Irian Jaya), Indonesia, and crossing it involves some preparations but is not that difficult as it might have been. In Jayapura, Indonesia, there is a consulate to apply for a tourist visa. The consulate is located in Mendi, a 10min green bus ride away from Jayapura's capital. As of August 2014 the tourist visas are free of charge. There's a currency exchange office nearby with good rates to buy kina.
Depending on your Indonesian visa there are different options to cross the border. If you have a visa on arrival, issued to you for example at the Jakarta Airport, you can only cross the border using a boat or by stamping out at customs in Jayapura and then immediately traveling to the border 30km away. Western travelers attempting the latter should expect to pay some miscellaneous fees and jump moderate bureaucratic hoops before leaving.
Boats can be rented from Hamedi.
Any other type of visa you can rent a car, or an ojek and cross the land border. If renting a vehicle for the crossing one should expect to pay approximately 300,000 rupiah from Jayapura town and travellers should expect to pay upwards of 500,000 rupiah to return from the border to Jayapura. Shared taxis to the border leave early in the morning from Pasar Youtefa, among other places. Alternatively, from the same place, you can catch a bemo to the village Koya Timur (half way to the border, 9000 rp, frequent departures) from where you can hire an ojek to the border for 70000 rp or try to hitchhike.
From the border to Vanimo a bus charges 10 kina. A few days a week there is a market at Batas, immediately on the Indonesian side of the border, that attracts many shoppers from PNG. IThe roads are busy on those days.
In April 2014, following a shooting, the land border was closed for any traffic. As of late July 2014 it seems to be back to normal. Travel by sea in banana boats is always an option, although more expensive.
Papua New Guinea is a strange place when it comes to travel. The tropical conditions, fierce geography, and lack of government capacity means there are very few paved roads in the country.
With the exception of a brief span of road connecting it to the immediate hinterland and a road that will enable you to follow the coast southeast for a few hours, there are no major roads linking Port Moresby to anywhere else.
On the north coast, a tenuous highway runs from Madang to Wewak only in theory.
The big exception to this is the Highlands Highway, which begins in Lae (the country's main port) and runs up into the highlands through Goroka to Mt. Hagen with a fork going back to the coast and Madang. Shortly outside Mt. Hagen the road branches, with southern line going through the Southern Highlands to Tari while the northern line runs through Enga province and ends in Porgera.
Minivan PMVs navigating muddy "highway" near Madang
By public motor vehicles (PMV)
The most common way to travel is by PMV/bus with the locals.
Lae, Madang, Goroka, Tari, and Mount Hagen are all connected by a good highway. As a newcomer it is probably advisable to get help from locals (e.g., hotel-staff). Most towns have several starting points. A trip from Lae to Madang costs around 20 Kina, to Mt. Hagen 30 Kina.
Papua New Guinea has historically been heavily reliant on aviation and still features some of the most spectacular flying in the world. In the 1920s, Lae was the busiest airport in the world - it was there that aviators in the gold mining industry first proved that it was commercially feasible to ship cargo (and not just people) by air. In fact, Lae was where Amelia Earhart set off on her last journey.
Air transport is still the most common way to get around between major settlements - indeed, pretty much every major settlement is built around an airstrip. In fact, the main drag of Mt. Hagen is the old airstrip! Travel from the coast into the Highlands is particularly spectacular (don't take your eyes off the window for a second!) and pilots from Australia, New Zealand, America and other countries work here just for the great flying experience. If you do not like small planes (or even smaller helicopters) however, flying to more remote locations here may not be the best option for you.
The two major domestic airlines are Air Niugini and Airlines PNG:
Air Niugini connects Port Moresby and, to a lesser extent, Lae with most of the provincial capitals, but does not offer much of a service between the smaller towns. A domestic route map is available. The airline flies Fokker F100s as well as smaller propeller planes.
Airlines PNG connects a large number of smaller centres. Planes with a seating capacity from 20 to 36. It operates on the mainland and does not serve the main outer islands. A route map is available.
Ferry from Madang to Wewak
Travel Air (aka Mangi belong ples) is usually cheaper and worth checking out. You can view prices and schedules on their website but you'll have to book at their office or agent.
People living in the archipelagos get around locally with the ubiquitous banana boat, a 30-40 ft fibreglass hull with an outboard motor. Popular routes are Vanimo to Aitape, Rabaul to New Ireland. Motorized canoes or banana boats are used on the big rivers.
Also, two or three shipping lines also sell tickets for passengers who want to leapfrog from one city to another. These ferries run only two or three times per week and offer upper and lower class. Upper gets you a bunk to sleep on while lower gets you a hard seat.
There is a ferry twice a week between Madang and Wewak. There are also ferries to Vanimo and from Madang to Manus. Also from Lae to Rabaul.
One small ship leaves the city of Lae once a week, stopping at Finschhafen and Umboi Island. Sleeping on the open deck of a ship as it crawls slowly through the South Pacific night is about as romantic as it sounds, but beware - it gets cold on the open ocean no matter where you are, so take some warm clothes or buy a cabin inside.
The government of Bougainville announced in June 2014 that it had purchased a ferry to do a weekly run Buka-Rabaul-Kimbe-Lae and back as of July 2014. However, in September 2014 the ferry was still being delivered. Besides, the government also purchased a smaller ferry to service the smaller Islands in Bougainville province.
There are a number of small ships that visit the islands of Papua New Guinea, including some of the most remote islands, such as Wild Earth Travel's True North, Silver Discoverer and Oceanic Discoverer.
The expedition ship the Spirit of Enderby visits Papua New Guinea every October and April.