Modified from an earlier answer which had a bit on training.

One of the advantages the Soviet Union had at the onset of Barbarossa and the subsequent losses during the campaign was that it had a large, state-wide apparatus for military service. The pressures of war, especially in the period 1941-1942, forced the training establishment to cut corners and feed recruits into the front. However, the notion that the Red Army overwhelmed the Germans with masses of troops with little to no training is inaccurate. Although barrier troops and other civilians dragooned into service did exist- see this excellent post by our all mighty moderator u/Georgy_K_Zhukov - such formations were not really reflective of the Red Army as a whole.

Conscription was an ever-present reality for many Soviet citizens from the establishment of the USSR. The Soviet state only allowed for conscientious objection from a few minority sects like the Doukhobors, so aside from health issues, there were few ways to escape the draft. So for a hypothetical Russian peasant (the Soviet Union was reluctant to expand conscription to its national minorities), compulsory military service would not have been something unexpected or extraordinary.

Up to 1935, the interwar Soviet army had two main forces, the krasnoarmeitsy (Red Army) were formal military men and terrarmeitsy (territorials) who were five year military reservists. The bulk of peasant military experience prior to the 1935 was spent with the terrarmeitsy, who would spend three months of training during the first year of service; two months in the second; and one month in each of his last three years. The Red Army underwent a doctrinal shift and began to transform all terrarmeitsy into formal military units by 1940. The terrarmeitsy provided a rudimentary groundwork for the conscription apparatus to expand greatly.

In 1940, the state passed a new military service law that massively expanded the size and scale of conscription. This caused a great deal of friction within peasant communities as the large casualties
from the Russo-Finnish War had became common knowledge. This unrest led to a greater crackdown on desertion and draft avoidance which only increased after the German invasion.

The scale of the German threat meant that the Soviet state resorted to many of the tactics it used to create the Red Army during the Civil War. Although lines of formal conscription remained, the state employed a wide degree of impressment and the resurrection of opolchenie (citizens militia army). The latter were volunteers and equipped with a hodgepodge of obsolete or captured weaponry. Training time could be as little as a few hours each day for a week before they saw combat. The closer to the front, the more chaotic conscription became; so called-front mobilization entailed military units impressing any military-aged male and putting them into the front line.

The state of conscription was less chaotic inside the Soviet interior, although that is not saying much In September 1941, the State Defense Committee established the Vsevobuch which provided formal military training within all localities of the Soviet Union. It established a minimum of 110 hours of training and opened 15000 training centers. In theory, the conscripts would form a reserve unit that would then be funneled in as replacements. The quality of training was often quite poor and the needs of the front forced
a telescoping of training. The 1943 account of Gabriel Temkin is instructive of this training (or lack thereof) for the Vsevobuch recruit. He spent enough time in his training depot to receive his military kit and no rifles, his trainer told him that he was to learn at the front. He describes his first combat as:

The politruk was right. There were plenty of rifles, ammunition, and hand grenades left by the dead and wounded in the field and trenches, and I was soon to “learn on the job” how to use them. I had not seen yet the first sunrise on the bridgehead when, before daybreak, and with no support from our artillery behind the river, our company was rushed into an attack on enemy positions.

In subsequent combat, Temkin's regiment suffered a thousand casualties.

Although Temkin's experience highlights the dangers of a constricted training regimen, his German opponents were also facing a manpower shortage and also had to cut corners. As the tide of the war turned, the Red Army was able to take a more relaxed attitude towards training and extend while their German opponent did not have this option. Allied Lend-Lease equipment, which often was more mechanically reliable than Soviet equipment, often got fed into the Soviet training establishment. Although there were still gaps in training, by the end of the war the bulk of the Red Army was a very well-trained and professional force.

Sources

Glantz, David M. Colossus Reborn: The Red Army at War : 1941-1943. Kansas: University Press of Kansas, 2005.

Reese, Roger R. The Soviet Military Experience A History of the Soviet Army, 1917-1991. London: New York, 2000.

Sanborn, Joshua A. Drafting the Russian Nation: Military Conscription, Total War, and Mass Politics, 1905-1925. DeKalb: Northern Illinois University Press, 2003.