By plane
North Korea's sole airline, Air Koryo, currently has scheduled flights from Beijing, which depart at 11:30AM every Tuesday and Saturday, and return from Pyongyang at 9AM on the same days. Air Koryo also flies to and from Shenyang every Wednesday and Saturday, and to Vladivostok every Tuesday morning.
Air Koryo is the only 1-star (worst) airline on Skytrax's list  and has been banned in the EU due to concerns over safety in the past, though is now allowed to fly in to EU territory again. To date, Air Koryo has only had one incident resulting in death, this was in Africa in 1983. The Air Koryo fleet consists largely of Soviet-made aircraft built between 1965 and 1990, plus the pride of their fleet, a 2008 Tupolev Tu-204, which now usually handles the core Beijing–Pyongyang route. Otherwise, you'll most likely end up on one of their four Ilyushin IL-62-Ms (1979-1988 vintage), but Air Koryo also flies Tu-154s dating back to the seventies and Tu-134s from 1983.
The only other airline with scheduled service to North Korea is Air China, which flies three times weekly from Beijing to Pyongyang. Neither Aeroflot nor China Southern continue to fly to North Korea. Air China is recommended above Air Koryo due to its far more modern and safe fleet.

By train
Train K27/K28 connect Pyongyang to Beijing in China via Tianjin, Tangshan, Beidaihe, Shanhaiguan, Jinzhou, Shenyang, Benxi, Fenghuangcheng, Dandong and Shinuiju four times a week. There is only one class on the international train between Beijing and Pyongyang: soft sleeper. It can be booked at the station in Beijing, but reservations must be made several days in advance. Your tour agency will usually do this for you, unless you are travelling on work purposes. It has been increasingly difficult to book space on the Beijing–Pyongyang route, so confirm your tickets well in advance.
Once a week train K27/K28 also conveys direct sleeping cars from Moscow via China to Pyongyang and vice versa. The route is Moscow - Novosibirsk - Irkutsk - Chita - Harbin - Shenyang - Dandong - Shinuiju - Pyongyang. Departure from Moscow is every Friday evening, arrival at Pyongyang is one week later on Friday evening. Departure from Pyongyang is Saturday morning, arrival at Moscow is Friday afternoon.
There is also a direct rail link into Russia, crossing the North Korean/Russian border at Tumangan/Khasan. This route is served by a direct sleeping car Moscow - Pyongyang and vice versa and runs twice monthly (11th and 25th from Moscow), arriving Pyongyang 9 days later. However, since the mid-nineties this has not been an officially permitted route for tourists, and KITC refuses to organize trips using this route; two Western tourists have been successful in taking this train into North Korea, but report that further trips on this route would unlikely be successful.

By boat
There is an unscheduled cargo-passenger ship between Wonsan and Niigata, Japan. Only available for use by some Japanese and North Korean nationals, the boat service has been suspended indefinitely due to North Korea's reported nuclear testing; Japan has banned all North Korean ships from entering Japanese ports, and has banned North Koreans from entering the country. Be careful about getting too close to the North Korean border in a boat; many South Korean fishermen are still waiting to leave North Korea.
Besides the unscheduled ferry there is also a cruise ship that operates between the coast of Northeastern China, and Mt. Kumgang. Joint operated by China and North Korea the cruise line uses a 40 year old ship. The cruise trip is 22 hours long at each leg, and is 44 hours long in total, but as a person outside of China you may not be allowed to go on the cruise to Mt. Kumgang.

By bus
A bus is theoretically available from Dandong, China, across the Yalu River to Sinuiju. It's run by the "Dandong China Travel Company" but is only open to Chinese citizens at present.