The standard book on this is called The Plot to Kill God by Paul Froese. Froese is a sociologist (and a good one), but it's a little bit of a strange book because he doesn't really speak Russian, so most of it based on secondary sources, if I recall properly. However, partially because of this, there's a heavy emphasis on surveys and statistics and you can really see where and how and when it was successful. The main campaigns were before WWII, as you may know, and by the late 30's the government had closed 90% of church buildings. Then, after the Nazi Invasion of the Soviet Union, Stalin briefly relaxed the restrictions on religion (especially Orthodoxy) as a way to unite the people against the Nazis (Islam was always dealt with a little differently in the Soviet Union).

Under Khrushchev, the Soviet Policy toward religion switched from repression to replacement, and there was a lot more focus on not only teaching scientific atheist but also in creating new, secular rituals (which had mixed success).

It's full of interesting tidbits, but I will say Froese is testing and advocating for a very specific theory (the economies of religion model), and I tend to be a supporter of the other theories that explain support for religion/secularization. One of the problems with the theory is it doesn't take into account the role of national identity, and how religious identity can often be imbricated with other identities. Forced secularization was least successful among groups where religion could be a focal point for group ["national"] resistance to the Soviets (Muslims of all stripes, Lithuanian Catholics, etc), as he repeatedly admits in the book. Unfortunately, I don't have the book in front of me so I can't quote the tables, etc. trying to measure how and where these things worked (and didn't work). However, though it's meant as an academic book, I know Froese also wanted laymen to be able to read it and get something out of, so if you're still curious about the topic, I'd recommend picking it up.

What methodology is available here? They didn't exactly do surveys or polls, did they?

I think this begs the question of: How successful were they in destroying the structure of religious groups in the Soviet Union? Or how successful were they in getting its individual citizens to stop being actively faithful? I don't think the 2nd comment can be answered substantively throughout the Soviet Union. I can only speak about the Muslim majority regions of the Soviet Union.
Soviet authorities began the campaigns against Religious organizations in Central Asia in the 1925 and accelerated in 1929. These campaigns focused on the tithing networks and Waqf system which supported religious organizations and religious figures.
Additionally, court reform created a local secular judicial system separated from the religious authorities. Following the seizure of the Waqf system, Soviet authorities regulated the individual activities of believers and banned religious education to children. Soviet authorities created an authorized religious structure and banned all unofficial religious practices in 1941. So, it is undeniable that Soviet authorities impacted religious beliefs and activities of its citizens but to what degree this affected personal religious beliefs, is still unanswered by historians. From Keller's Moscow Not Mecca: "Brute tactics also turned out not to work in the plain sense, either. Mosques that were technically closed actually functioned, women who unveiled at party meetings reveiled to walk back home, clergy evaded taxes, and religious tenets continued to be taught after Muslim schools were closed, sometimes by teachers in Soviet schools." From another page: "When local municipal service agencies began to seize waqf assets from Narkompros, the state was almost powerless to stop them. As a result of the seizures, state plans to use waqf income to build a secular school system was largely sabotaged." So it is undeniable that Soviet policies affected the practice of religion within the Soviet Union, so the question of how much that affected the individual beliefs of Muslims or religious peoples within the Soviet Union- is still unanswered. Sources: Shoshana Keller, Moscow Not Mecca Khalid Abeed, Islam After communism. For any interested people in Central Asian identity: Ali Igmen, Speaking Soviet with an Accent.