Edited from.an earlier answer I wrote to a similar question:

The Soviet military (it was renamed from the Red Army from 1946 on) was already undergoing massive and comprehensive changes even before the final collapse of the Soviet government. Gorbachev had publicly called for a total reduction in Soviet military personnel by 500,000 in November 1988, and by 1991 cuts in total personnel numbers by an additional million were discussed. Between 1990 and 1993, the number of servicemembers in the Soviet-then-Russian Federation military effectively halved, going from about four million to two million (military forces in the other republics were likewise mostly very small and declining in size).

Some 15 divisions in Central and Eastern Europe and Mongolia were being withdrawn and in many cases disbanded (some 37 tank and motorized divisions were disbanded between 1989 and 1991). The Conventional Forces in Europe Treaty had been signed in November 1990, and although it didn't come into force until 1992, there was already a move to redeploy military forces and material east of the Urals in compliance with the treaty's requirements.

This dislocation was accompanied by a sharp decline in popular prestige for military service - much of this came about through glasnost's loosening of media reporting on military affairs, and widespread popular disaffection with dedovshchina and the war in Afghanistan. Crime against military personnel increased sharply after 1989, and draft-dodging became a serious and widespread issue from fall 1989 on - by late 1991, some 20 percent of those called up for duty refused to report. Education deferrments meant that those who reported for duty tended to be poorer and less-educated, and increasing ethnic tensions between different national groups usually followed conscripts into the barracks. Massive budget cuts at the Soviet government level and republic level meant that those serving put up with inferior housing, and often a lack of basic food goods like meat, dairy or vegetables.

Long-standing discipline issues among conscripts worsened. The older year of two-year term conscripts was notorious for its beating, hazing, and general horrible treatment of the newer, incoming year - this is the infamous dedovshchina, or "rule of the grandfathers", which has afflicted post-Soviet military personnel as well This was a real, literal hazard: it's estimated that more conscripts died from this abuse - about 15,000 - in the last five years of the USSR than were killed in combat in the almost ten years of fighting in Afghanistan.

In a deteriorating stare, the Union-wide military structure more or less existed after the technical end of the USSR, with the idea advanced by the last Soviet Minster of Defense (Marshal Yevgeny Shaposhnikov) that the military would report to all heads of state in the new Commonwealth of Independent States, which in December 1991 effectively meant all of the former SSRs except for Georgia and the Baltics. This would have been vaguely similar to how NATO has a unified command, but also would have been incredibly unwieldy.

One reason this plan was almost immediately scuppered is that first the government of Ukraine under Leonid Kravchuk and then the Russian government under Boris Yeltsin. Kravchuk had insisted on any officers on Ukrainian territory swearing an oath of loyalty to the Ukrainian state, and had also fired senior officers serving on Ukrainian territory and replaced them with allies. Every other CIS state except Russia established its own Ministry of Defense in this period, and eventually Yeltsin got tired of trying to maintain a CIS-wide institution at Russian expense - he organized his own Russian Ministry of Defense in March 1992, with himself as Defense Minister, and by May of that year had appointed a Shaposhnikov rival (Pavel Grachev) to the position, formally established a Russian Armed Forces, and required all military personnel on Russian territory to swear allegiance to the Russian Federation. The idea of a CIS-wide armed forces with Shaposhnikov as its head existed on paper until June 1993.

It's also worth noting that the situation of the Soviet military differed based on which republic one was in. The major units were in Russia, Ukraine, Belarus and Kazakhstan (out of some 130 manuever divisions active in 1991, 71 were in Russia, 20 in Ukraine and 10 in Belarus) - Ukraine in fact had some of the best-equipped military units, especially as these tended to be the Soviet forces that were most-recently withdrawn from Central and Eastern Europe. These units, as shown in Ukraine's case, fell under the control of their "home" republic's government, which made sure that these units were commanded by officers loyal to the new country. In other cases, the outcome was a little different: in Tajikistan, the Soviet military units remained effectively under Russian control and were directly integrated into the Russian military once that was established, but that country was already being torn apart by a civil war. Soviet military units in the Baltics and Georgia also wound up under Russian control, but were treated as occupying forces to be withdrawn. In Moldova, the Soviet military took sides with Transdnistrian separatists, and then stayed (as part of the Russian military) as "peacekeepers" - a similar process occurred in Abkhazia.

So in short: for someone in the Soviet military, the increasing institutional mess that had really started around 1989 really picked up pace in late 1991, but there were strong continuities into 1992 and even 1993. Probably your bigger issue would be the lack of or insufficiency of pay or housing, and trying to literally survive brutal treatment at the hands of older enlisted personnel and officers.