There are many variables on how it could go ranging from support within NK to our planning process.
NK doesn’t really constitute a threat per se, since their equipment we can pick off with airpower for the most part. But it's the Special Forces, which NK has a lot of we have to watch out for. They are not blind to our situation in Iraq, and would modify their tactics, techniques and procedures for use in NK.
The Air Force and Navy is a joke, while the Army only has manpower on their side...not very good force multipliers against a highly advanced and technological foe. They have considerable fuel problems, maintenance problems, and sometimes can't even feed their people/soldiers. Despite the terrain of NK, which will constraint our movement, we have a battle-harden force from our experiences in Iraq and Afghanistan.
The loyalty to the regime will be the biggest question...if we wipe out all the key leadership in a couple strikes, NK for the most part may fall rather quickly. However it could go the other way as well.
The biggest problem would be taking out all of the artillery along the NK SK border, with over 5,000 pieces, 75% aimed at Seoul, SK will take some considerable damage at the outbreak of hostilities. There are more advanced studies out there about NK which of course cannot be talked about but for the most part this is how it is.
The best way for NK to integrate into SK would be through a seamless transition...through the use of propaganda and massive aid/construction programs...if we show them progress, they will be more likely to support us in the long run.
This is just a quick synopsis on the problem. (And not mentioning China at all)
The major parts of the war would be over quickly (not as fast as Iraq, and also depending on when attack is launched due to seasonal variances) however, the peace sustaining operations would involve the most planning and analysis of the situation. The entire country won’t be pacified when we take it over however there won’t be any major Force-on-Force battles, just die-hards of the regime, and some regional hold-outs we bypassed.
SK would need substantial aid in order to integrate NK into SK society. It would take perhaps up to a decade for the infrastructure to be built, and you will also need to educate people as well. NK won’t reach a level of SK standard of living for around 25 years. For example just look at West/East Germany and the problems associated with the unification. It would be much worse with Korea.
