In short - quite badly.
This is mostly an edited repost from a while back where I explain the difference between the regimes of different generations of the Kim dynasty, but it covers similar themes.
North Korea, by the late 1970s, had a dysfunctional economy that failed simply because it was a Leninist system - the reasons are the same as everywhere else: distorted price info, lack of innovation (and incentives to innovate), and so on. North Korea exacerbated these inherent problems by maintaining an anomalously high level of military spending and relying on an ideology that basically propagated the creation of an autarky.
To make matters worse, it came to rely (ironically in no small part due to its refusal to accept an economic specialization and aiming to reduce its dependence on imported products and goods) on Chinese and Soviet aid for the survival of its economy. The scale of this support can never be estimated with real precision, since much of this aid was provided indirectly, through subsidized trade. As long as the Soviet Union and China, driven by their own geopolitical considerations, were willing to pump this aid in, the North Korean economy remained afloat, even though its growth rate was decelerating.
You can guess then, what happened when the foreign aid started to dry up - as the relations between Moscow and Beijing (as well as between Moscow and Washington and Beijing and Washington) became more and more amicable, the need to maintain North Korea first as a buffer zone against the US and a neutral zone in the midst of the Sino-Soviet split, was fading. By the late 1980s both China and the Soviet Union were liberalizing their economies and the "trade" with North Korea was becoming more and more pointless (as it was basically non-reciprocal) as political considerations evaporated.
By the time the Soviet Union collapsed, it ceded its place as the largest foreign donor to the People's Republic of China, but the amount of aid that it provided was still substantial.
This disruption of foreign aid led to a literal collapse of state economy. By the year 2000 the industrial output fell to roughly half of what it was in 1990.
The agricultural sector was hit particularly hard as it relied very heavily on Soviet fertilizers and artificial irrigation (which relied on electricity, which relied on "imported"/gifted gas from China or the USSR). To make matters worse the torrential rains of 1995 and 1996 wrecked havoc on North Korean fields (which were terraced). All this provided a backdrop for a sudden termination of the so-called PDS (public distribution system) that has been in place since 1957. The PDS basically ensured that the North Korean populations received their food - it being the major (or even, in some cases, only) source of food for the majority of the population. By 1993-94 the rations were increasingly delayed and decreased in size. After the floods they stopped almost completely.
For the average North Koreans this was a disaster. A twice-monthly trip to the grain distribution center was as normal as a weekend drive to a supermarket for an American family. To this day we don't know how many people perished during the famine of 1996-1999, but some NGOs estimate that as many as 3 million people starved to death (most scholars tend to agree that it was somewhere between 600.000 and 1 million).
This is the single most important economic consequence of the sudden deterioration of the Soviet aid. This major downturn was not caused by the collapse of the Soviet Union, but it exacerbated things for sure.
Good further reading:
Hi /u/Bluegutsoup! I got a similar question in our AMA on Korean history last year. I answered it here, although I do focus mostly on the 1994-1998 famine, which was the most visible and horrific result of the U.S.S.R.'s collapse and withdrawal of support for North Korea's economy.
Is there anything else you'd like to know? NK has arguably never really recovered from the end of the Soviet Union, so it's a complicated subject.