1945

USSR agrees to join the Pacific War against Japan.

United States drops the atomic bombs, Russia rushes in as fast as they can to get Sakhalin, Manchuria, and Korea up to the 38th parallel, the agreed upon dividing line.

Japan is defeated, the US goes to South Korea.

The Cold War starts.

Kim Il-sung is installed as a Russian puppet, Syngman Rhee is installed not so much as a puppet, but because the US didn't really know any better.

1948

UN elections are boycotted by the North in 1948. South Korea elects a government and North Korea elects their own. Both the ROK and DPRK are founded in late summer of 1948.

Both Kim and Rhee want to reunify the country under their respective regimes. Kim is given weapons and training by the USSR and experienced North Korean soldiers from the Chinese Civil War. Rhee is given virtually nothing by the US because he would have totally started the Korean War if he could have - the US wanted to keep him reigned in.

1950

Kim got permission and support from Russia and China and he started the Korean War. The US/UN forces came in and forced a stalemate in 1953. During that time, the US dropped 635,000 TONS of bombs on North Korea during the war. During the whole Pacific campaign, the US dropped 503,000 tons. Ten percent of the North Korean population died.

To put this in perspective, think about Bush/Obama and drones. Obama had more drone strikes in a year than Bush had in 8, because the technology was developed under Bush. It's the same thing here - WWI bombing was guys in bi-planes with dynamite and grenades. World War II saw the introduction of long range strategic bombers on an industrial scale - B-17's and B-29's. By the time the Korean War started, strategic bombing had been perfected in places like Tokyo, Dresden, and Berlin. Furthermore, the Pacific campaign involved island hopping. Cruisers and destroyers would pummel islands from the sea. The majority of bombs dropped in the Pacific were bombing of Japanese cities. So while it's impressive, it's also comparing apples and oranges - bombers flew from Japanese bases to Korea and hit both military and civilian targets. Strategic bombing was possible from day 1.

1953 onward

The war ends, POW's are exchanged, both sides begin rebuilding. North Korea got more aid short term than South Korea. They also were rebuilding factories, dams, and other industrial capability that the Japanese had built during the colonial era. South Korea was building these things from scratch. North Korea played China and the USSR against each other in attempts to remain free from both sides and squeeze as much aid as possible. South Korea, on the other hand, developed a solid relationship with the US. Politically, things were dicey - Rhee was ousted in 1960, a weak government took over that was ousted in 1961 by Park Chung-hee. Park was/is a controversial figure. He helped build up the south economically, but he was also a harsh autocrat who had people killed.

How did the South and North take different directions? Kim and family built a cult of personality around themselves and they purged those who disagreed with them. This sucks when Kim has no clue about farming and someone says, "well, it might be better if we..." A guy who knows what to do is killed, a bad policy is implemented, and people suffer. In the South, Park definitely had cronies, but he demanded results and he got them. The government supported the chaebols, the large conglomerates, to build the economy. People got jobs, stuff was made, people made money, living standards improved.

1980s-1990s

Now, to be fair, standards of living were better in the North until the mid 70's to early 80's (it depends what sources you cite, but it was in that time period where the South's economy overtook the North's - mid 70's by a few measures, early 80's by all measures). In the 80's, South Koreans overthrew the military regime and elected a civilian government. North Korea elevated Kim Jong-il more and more until his father's death in 1994, when he became the Supreme Leader. In the mid 90s, flooding caused widespread famine in the North, where trees had been cut down for fuel, so mudslides killed people and crops washed away and loads of people died. In the South, the Korean Forest Service had planted loads of trees, and sustainable farming practices meant that there were no mudslides or crops washing away, at least not at the level as in the north.

How did the North become a dictatorship?

First, the South was a dictatorship, too. There were rigged elections, people murdered, money stolen, etc. Rhee was a power hungry guy who rigged the 1960 election for his hand-picked successor. This led to an uprising which overthrew the government. Park Chung-hee staged a coup in 1961. He DID resign from the military and run as a civilian in the election, but the elections were all pretty shady, each one getting worse and worse. It wasn't until 1987 that the first truly free elections were held (and the liberals ran two candidates, so the military leader's choice won anyway! HA!) and it wasn't until 1993 that a liberal civilian became president.

But as far as North Korea goes, the Kim family did what Stalin and Mao did. They built a cult of personality, they purged their enemies, and they've maintained their grip on power. Not too much to it.

If you're looking for a basic introduction to Korean history, I'd recommend A History of Korea by Kyung Moon Hwang. The chapters are short and easy to read - the whole book is only a few hundred pages and it covers all of Korean history - and it gives the main highlights. For information on the Kim family and how they became and stayed leaders, check out Under the Loving Care of the Fatherly Leader by Bradley K. Martin. It's the authoritative text on the subject.