I have been watching Enemy at the Gates and I am curious about the curacy of the movie.
With regards to the very early stages of the war, some parts of Enemy at the Gates are a little accurate, but that phase didn't last long. The USSR purged most of its competent officers in 37-38, and suffered disasters in '41, losing much men, industry, and equipment. In the Russian "recovery period" (41-42), they used enormously crude tactics. Stalin forbade civilians to leave Stalingrad since he reasoned his army would fight harder for a live than a dead city.
Soviet doctrine in 36 was the most brilliant in all of Europe. Developed from experience in the Russian civil war and war against Poland, their doctrine was called "deep operations", and rested on the following assumptions:
Officers are executors of orders, and high command should be responsible for making the big decisions.
Forces should be concentrated and categorized - artillery, infantry, cavalry, to make them easier to command and more organized.
Zeal determined morale in war, and propaganda is of the essence. Morale made a huge difference.
Absolute discipline, through summary executions if needed, maintains morale and cohesion.
Once an enemy line is broken, following up the opening with reserves created impressive results.
Armies should recklessly move forwards once a line is broken and race to the enemy's vulnerable rear.
Infantry should be used to probe and test the enemy attacks and determine where to commit reserves.
Resources from failing initiatives should be directed to successful ones.
Forces are better suited sticking to the overall plan instead of improvising to win small victories - the idea of the "operational art" over the pure tactical art.
When armor came along, it should be concentrated in distinct divisions.
Logistics are of the essence and should be as mechanized as possible to enable a rapid advance and "leapfrogging" of divisions - a constant advance racing into enemy territory faster than they can retreat.
This system collapsed when Tukhachevsky and his crew were purged. Russian doctrine in 1938-41 essentially made it the France of the East. Armored divisions were split up, and their tanks were idiotically spread among infantry. The replacements in high command had almost no understanding of deep operations.
By 1942, however, the Soviets had once again found their element. Starting with the envelopment of Stalingrad, the Soviets used the following tactics:
Offensive
STAVKA, the general staff and top officers, would assign some of their personnel to a front to study an offensive point.
Rocket artillery, regular artillery, and aircraft, especially the formidable Il-2 "flying tank", would massively bombard the area to soften up resistance
Infantry waves would be launched to figure out weak points in the line, across a broad front - this being called the 'first echelon'
In these narrow salients, tanks and reserves, a 'second echelon', would penetrate deep, causing the collapse of the enemy front.
Strongpoints and cities would be largely bypassed and ignored
Divisions would 'leapfrog' as far as they could, stopping to refuel and fix up as another continued the attack.
Defensive: Defense in Depth
The Soviets laid land mines, funneling tanks into "kill zones" where artillery and tanks would engage them
There existed multiple lines of defense
Once an enemy weak point is discovered through their sluggish progress in that sector or probing counterattacks, the Soviets thrust their reserve into that sector, ending the enemy's offensive.
The Soviets by 43 were actually very advanced, and inflicted more casualties on the Germans than they suffered themselves in 44 and 45. They launched rapid invasions of thousands of miles of territory, inflicting more casualties on the Germans than they sustained themselves in Belgrade, Romania, Hungary, Czechosloakia, and Konigsberg, and trapping hundreds of thousands of Germans in the Courland pocket.
Unlike the Germans, the Soviets emphasized motorization, allowing them to adequately supply their forces far from home and continuing sweeping operations.
If you were to make a hollywood movie out of all of this, it would be very boring though! Men bombard an enemy position with artillery, then a first wave is slaughtered, but some men make it over the hill and take the position! A man from STAVKA arrives and announces this sector is a weak point in the enemy line. Within hours, hundreds of planes would rush overhead, and hundreds of tanks would sweep across the snows and penetrate. Men would climb onto these tanks, or in unprotected trucks, and drive for literal hundreds of kilometers, with the tanks and planes sweeping aside much opposition. Infantry would dismount from the tanks and trucks in combat, and, assisted by them, attack enemy positions that the army needs to move past, in firefights lasting hours at a time, usually in long, rural battlefields over huge distances.
I don't have a good reference for Soviet tactics in 1941-1942 but the question about how realistic the 'tactics' shown in the film Enemy at the Gates comes up from time to time. See this response for example on the question of whether unarmed human waves was really a thing or not.
In the book "Enemy at the Gates, the Battle for Stalingrad", William Craig explains in detail how the events played out. While there was some artistic license taken in the movie, the vast majority of the major events are factual. There was a very accomplished Russian sniper by the name of Vassili Zaitsev. He trained his girlfriend to be a sniper as well. The Germans did send a counter sniper by the name of Erwin Konig and there was a lengthy battle of patience where Zaitsev eventually got the upper hand. The man who accompanied Zaitsev on his missions took a bullet in the shoulder in order to give away Konigs position. There was even a young boy named Sascha who passed intelligence to the German army and was eventually hanged by the Germans as they were retreating. If you're referring to the movies opening scene where the Russian soldiers are shot for cowardice, Craig relates the case of a Russian commander who had his troops form a straight line. The commander filled a revolver as he chastised them for their cowardice. He then proceeded to walk parallel to the line while counting to 10. On every 10th man he put the revolver to their head and shot. He did this until the gun was empty then dismissed the remaining troops.