(OK, here's primary and secondary sources)
Brief answer:
Life didn't change noticeably for average citizen for ~5 years.
Detailed:
Death of Stalin was felt by many millions as personal tragedy. People cried - literally for hours. When the burial ceremony was held, so many were trying to attend (~2 millions), that many were crushed to death in the crowd - just too many people went to Kremlin.
One small group of people who experienced almost immediate change were "doctors-poisoners" (Дело врачей = Doctor Affair - see [4]) - by April 3rd all who were still under investigation, not sentenced yet, were set free and charges dismissed.
Most important event of 1953 after Stalin death: "Beria's amnesty". By March of 1953, there were ~2.5 millions in GULAG (precisely, 2 526 402). Of those, Beria proposed to free immediately with up to 5 years sentences ( in his Politburo memo (March 23rd, 1953). And longer sentences were to be commuted in half. "Especially dangerous convicts", "convicted for banditry and terrorism" with 10-25 year sentences were excluded. Many high-level trotskists, right-leaners, foreign spies, bourgeois nationalists were in these categories and thus ineligible (221 435). Total number of affected by amnesty is difficult to calculate, as decision to commute sentence was at local authorities discretion, ~1.2 millions (e.g. total number of released+commuted sentences - see [3]).
Politburo agreed and, by summer of 1953, almost all with "light sentences" were freed. Crime rate jumped up - as amnesty didn't distinguish between political prisoners and criminals.
Life certainly changed for the top leadership - it was immediately engaged in intense struggle for power. Beria lost to Malenkov and was really "last repressed for political reasons and shot by firing squad". Then gradually Khruschev risen to power by 1955, pushing away Malenkov and Bulganin.
I cannot possibly try to cover everything in USSR even for 53-55 period without writing a book, so if you want to know anything specific about that time, please ask.
Sources
RIA Novosti - Moscow - Street crowd. Gorky street, Moscow downtown, ~10 min walk to the Red Square.
Images from RIA Novosti archives, search "похороны+сталина" = "stalin burial"
Photo - Penza - Street ceremony at the same time as burial in Moscow
russian - Amnesty of 1953. "Russian Amnesty" website.
Orlando Figes - Whisperers: Private Life in Stalin's Russia. Secondary source and with very narrow focus - as it dwells on just several families with repressed members, without looking at everyday life in USSR at large, outside of GULAG. Still, it describes amnesty.
Can I ask the additional question of asking what happened to the prisoners in the gulags? Were they forced to serve their time or were they released straight after Stalins death?
