I'm going to try to keep this brief because I'm far too hungover to be emptying my bookshelf but, in a word, life under Stalinism was hard. To spend a few more words, Alec Nove has referred to the period of the FFYP as "the most precipitous decline in living standards known in recorded history".
Like all 'life like for X' requests, this is a potentially massive question. To narrow the scope, I'll focus on living standards amongst the urban proletariat and the resulting social impact. That means I'll avoid or touch lightly on the peasantry, mass violence, Stalinist culture, late Stalinism, the famines, social mobility, etc.
I'm also going to skip over the question of social identity itself. This does warrant a note though: plenty of the terms used before (including 'proletariat') were highly charged politically at the time. Often we view Soviet society through the state's own lens: we pay attention to slogans, workplaces and plans because that was how the state observed and ordered society. Just a disclaimer to consider when going through the below.
But first let's note that the Five Year Plans (FYPs) essentially threw the country into an orgy of construction. This was a time of severe dislocation, in every sense. The industrial workforce tripled between 1928 and 1940 (4m - 13m) as peasants flooded into newly built factories and cities. The cultural, political and agricultural revolutions were just as jarring. But if this was movement then it was only loosely coordinated. For all its talk of 'plans' the Stalinist system placed great emphasis on 'shock' and energy; of getting things done regardless of the constraints and consequences. Much of of what follows below is the product of this wasteful shock.
Living Standards
One consequence of this was that living standards, as noted above, plunged during the industrialisation drive. Estimates differ but Chapman's figures for wages are widely accepted: they show that urban real wages in 1937 were only 58-85% of those of 1928 (depending on the price weight used). This hides an even sharper fall during the crisis of 1931-33, when agricultural crisis led to a severe shortage of food in the cities. Rationing was introduced in 1929-34. By Chapman's estimates, real wages for workers wouldn't recover their 1928 value until after Stalin's death.
(This wasn't helped by the practice of extracting regular 'voluntary' bonds from the workers. These were effectively loans to the state that would never be repaid and, on average, amounted to about a month's wages annually.)
It was at the same time that shortages became a permanent feature of the Soviet economy. They became, to quote Fitzpatrick, "a central fact of economic and daily life." Mark Harrison notes that the share of the net national product consumed by households almost halved in the 1930s, as consumer goods industries were starved of investment as capital was directed towards industrialisation. This tightening of belts was literal in the case of nutrition: average worker calorie consumption in 1937 was almost certainly less than in 1913 and infant mortality rose through the 1930s.
In addition to this, the housing crisis went from worse to worse. The influx of millions of peasants into the cities entirely overwhelmed the (chronically underfunded) public authorities. Families were crammed into accommodation, with apartments shared between several families, while in the new industrial towns springing up workers slept in cold barracks.
Social Impact
Whatever about official proclamations, the above was partly design. Drawing from 1920s practices, worker bodies were instructed to "face towards production". Hitting production targets was the new holy grail and unions, party cells and factory management were all expected to support this. Striking was illegal, quality suffered, work was intensified, piece rates continually rose, etc. The picture that comes through is of a steady intensification of labour in the name of 'productivism'. As the war loomed, draconian labour laws were introduced that promised punishment for being late for work or changing jobs without permission.
But that's just one aspect. The Stalinist regime employed brutal repression but it couldn't survive merely on that. Partly all the above was alleviated by the sheer inefficiency of the system: desperate to maintain skilled workers, factory directors often looked the other way when it came to minor offence. Factory canteens took a central role in providing for families. Peasants moving to the cities certainly fared better than they would have if remaining at home. The severe labour shortages meant that there was always a degree of give-and-take at shop floor level. Indeed, Filtzer has argued that the introduction of increasing severe labour legislation was proof of the state's inability to control its workforce.
Above all, for established workers there was the potential for promotion into the elite itself. By 1933, some 10% of the 1930 industrial workforce had 'graduated' into technical or administrative positions. These promotees (vydvizhentsy) would form a major basis of support for the regime and effectively provide its ruling cohort for the rest of the century.
Summary
So much for brief. What should hopefully be apparent is that these were years of extreme dislocation and hardship for society. Few escaped untouched from this 'revolution from above' but I've just noted a handful of the ways in which lived changed drastically during the 1930s. This did begin to ease up slightly as the economy improved in 1936-37, and society recovered from the disaster of 1932-33, but the preparations for war in the Third Plan marked a return to harshness. It wasn't until Stalin's death that the economy fundamentally shifted from an administrative/repressive focus on heavy industry to an emphasis on (partially) meeting consumer demands.
Sources
If you want a 'from below' view of Stalinism then Fitzpatrick's Everyday Stalinism should be your first stop. Closely followed by Filtzer's Soviet Workers and Stalinist Industrialisation. Rossman (Worker Resistance Under Stalin) and Murphy (Revolution and Counter-Revolution) provide more case-study led examinations of shop floor relations.
From an economic viewpoint, Alec Nove's Economic History of the USSR is always the best starting-point, with Davies et al's Economic Transformation of the Soviet Union also invaluable. In addition to these, I drew on Davies' Crisis and Progress in the Soviet Economy and Wheatcroft's Russian and Soviet Living Standards.