A ferry on the Congo River operates, if security permits, from Kinshasa to Kisangani, every week or two. You can pick it up at a few stops enroute, though you have to rush as it doesn't wait. A suitable bribe to the ferry boss secures a four bunk cabin and cafeteria food. The ferry consists of 4 or so barges are tied around a central ferry, with the barges used as a floating market. As the ferry proceeds wood canoes paddled by locals appear from the surrounding jungle with local produce - vegetables, pigs, monkeys, etc - which are traded for industrial goods like medicine or clothes. You sit on the roof watching as wonderful African music booms out. Of course it is not clean, comfortable or safe. It is however one of the world's great adventures.
The few trains which still operate in the DRC are in very poor condition and run on tracks laid by the Belgian colonial government over a half century ago. The rolling stock is very old and dilapidated. You are lucky to get a hard seat and even luckier if your train has a dining car which probably has limited options that run out halfway through the trip. Expect the car to be overcrowded with many sitting on the roof. Trains in the DRC operate on an erratic schedule due to lack of funds or fuel and repairs/breakdowns that are frequent. On many lines, there can be 2-3 weeks between trains. If there's any upside, there haven't been too many deaths due to derailments probably less than have died in airplane crashes in the DRC. There's really no way to book a train ride in advance; simply show up at the station and ask the stationmaster when the next train will run and buy a ticket on the day it leaves. The Chinese government in return for mining rights has agreed to construct US$9 billion in railroads and highways, but there is little to show for this as of 2012.
As of 2012, the following lines are in operation...but as mentioned above, that doesn't imply frequent service:
Kinshasa-MatadiBuilt in the 1890s by forced labor of whom 7000 died, this line is the busiest in the country. There is possibly once or twice weekly service.
Lubumbashi-IleboPossible weekly service, with the journey taking 6-8 days. In 2007, the Chinese agreed to extend the line to Kinshasa, but current progress in unknown. Ilebo lies at the end of the navigable portion of the Kasai River, allowing travelers to transfer to ferry to reach Western DRC.
Kamina-KinduUnusable after the war, this line has been recently rehabilitated. The line connects with the Lubumbashi-Ilebo line, so there may be trains running from Lubumbashi-Kindu.
Kisangani-UbunduA portage line to bypass the Stanley Falls on the Congo, service only runs when there is freight to carry when a boat arrives at either end which may be once every 1-2 months. There are no passenger ferries from Ubundu to Kindu, but you may be able to catch a ride on a cargo boat.
Bumba-IsiroAn isolated, narrow-guage line in the northern jungles, service has restarted on a small western section from Bumba-Aketi and possibly Buta. There were reports of trains running in the eastern section in 2008, but this part is most likely abandoned.
Lines that are most likely inoperable or very degraded/abandoned are:
A branch of the Lubumbashi-Ilebo line that runs to the Angolan border. It once connected with Angola's Benguela railway and ran to the Atlantic until the 1970s when the Angolan side was destroyed by a civil war. The western half of the Benguela railway has been rehabilitated and may be operational to the DRC border in the future.
The Kabalo-Kalemie line runs from the Kamina-Kindu line at Kabalo to Kalemie on Lake Tanganyika. The easternmost section has been abandoned. Although unlikely, there may be service on the western half of the line.
Due to the immense size of the country, the terrible state of the roads and the poor security situation, the only way to get around the country quickly is by plane. This is not to say that it's safe — Congolese planes crash with depressing regularity, with eight recorded crashes in 2007 alone — but it's still a better alternative to traveling overland or by boat.
The largest and longest-operating carrier is Compagnie Africain d'Aviation (http://www.caacongo.com/), with service to Goma, Kananga, Kindu, Kinshasa-N'djili, Kisangani, Lubumbashi, Mbandaka, Mbuji-Maya, & EntebbeKampala, Uganda.
Formed in 2011, Stellar Airlines (http://stellarairways.com/) operates one Airbus A320 plane between Kinshasa-N'djili and Goma and Lubumbashi.
FlyCongo (http://flycongo.com/) was formed in 2012 from the remnants of former national airline Hewa Bora, operating from Kinshasa-N'djili to Gemena, Goma, Kisangani, Lubumbashi, & Mbandaka.
Lignes Aeriennes Congolaises (http://www.lacrdc.com/) flies to Goma, Lubumbashi, Kindu, Kinshasa-N'djili, Kisangani, & Mbuji-Maya.
Air Kasaï (http://www.airkasai.cd/) operates from Kinshasa-N'Dolo to Beni, Bunia, Goma, & Lubumbashi.
Korongo Airlines (http://flykorongo.com/ind...) began operations in 2012 from its base in Lubumbashi to Kinshasa-N'djili and Johannesburg, with routes to Kolwezi and Mbuji-Maya planned for summer 2012. Maintenance for Korongo is carried out by Brussels Airlines, so its probably the safest choice.
Congo Express (http://www.flyexpress.aero/) was formed in 2010 and flies only between Lubumbashi and Kinshasa.
Wimbi Dira Airways was once the second-largest carrier, but does not appear to be operating as of June 2012. Others that may or may not be operating are: Air Tropiques, Filair, Free Airlines, and Malift Air all operating out of Kinshasa-N'Dolo airport.
As smaller vehicles are unable to negotiate what remains of the roads, a lot of travel in the Congo is done by truck. If you go to a truck park, normally near the market, you should be able to find a truck driver to take you where ever you want, conflict zones aside. You travel on top of the load with a large number of others. If you pick a truck carrying bags of something soft like peanuts it can be quite comfortable. Beer trucks are not. If the trip takes days then comfort can be vital, especially if the truck goes all night. It helps to sit along the back, as the driver will not stop just because you want the toilet. The cost has to be negotiated so ask hotel staff first and try not to pay more than twice the local rate. Sometimes the inside seat is available. Food can be bought from the driver, though they normally stop at roadside stalls every 5/6 hours. Departure time are normally at the start or end of the day, though time is very flexible. It helps to make arrangements the day before. It is best to travel with a few others. Women should never ever travel alone. Some roads have major bandit problems so check carefully before going.
At army checkpoints locals are often hassled for bribes. Foreigners are normally left alone, but prepare some kind of bribe just in case. By the middle of the afternoon the soldiers can be drunk so be very careful and very polite. Never lose your temper.