In August of 1945, the Strategy Policy Committee at the Pentagon assigned two men, Dean Rusk (until recently a Colonel, but then of the State Department) and Colonel Charles Bonesteel, to work out an occupation zone in Korea for the United States.

Recognizing that the Soviets would expect a share of Korea, they consulted a map and decided on the 38th parallel. It had two advantages; firstly it divided the country more or less equally in half, and secondly it left Seoul in the American zone.

A few things should be remembered here. The first is that the Soviets were very nearly in Korea by this point, and were in a position to occupy nearly the whole peninsula before the US could get there, if no compromise with them could be reached.

The second is that Bonesteel and Rusk had no detailed maps of Korea to work from, and were under serious time pressure. According to Rusk, the map they ended up using was actually from a copy of National Geographic. (The anecdote appears in his memoir, As I Saw It.)

In essence, they winged it. They simply didn't have time to do anything more.

You ask whether there were any other serious proposals, and yes, I'm aware of one. Reviewing Bonesteel and Rusk's work the next morning, Admiral Gardner suggested the 39th parallel, which would include most of Korea and parts of Manchuria's Liaodong Peninsula. The Liaodong Peninsula included Dairen—the most northerly warm-water port city in China. The Russians had always desperately sought warm-water Pacific ports, since their own most southerly major port, Vladivostok, was unusable in the winter. They had in fact leased Dairen from China in the 1890's—a lease which strongly contributed to the tensions that led to the Russo-Japanese War in 1904; a war which began with a surprise attack at Dairen.

In any event, it was decided that the Soviets would be unlikely to accept the 39th parallel, and so Bonesteel and Rusk's original suggestion of the 38th was sent to Stalin. Stalin acquiesced, although he took the opportunity to remind the US that they would not accept American occupation of Dairen, even though they'd gone out of their way not ask for it.

There was also a possibility that China and Britain might have been granted zones, in a quadripartite arrangement, by I'm not sure that that was ever more than hypothetical. I don't know that anyone ever actually proposed it seriously.

Finally, you ask how it was implemented. Well, when the Soviets advanced to the 38th parallel, they stopped marching. Then the Americans landed and collected the surrender of Japanese forces on remainder of the peninsula.

Anyway, check As I Saw It for Rusk's anecdote about Nat Geo. For a quick overview of it, including Gardner's proposal of the 39th and the correspondence with Stalin, check Policy and Direction : United States Army in the Korean War, by James Schnabel. Here's a direct link.