There were all kinds of ways, perpetrated by all kinds of people, in all kinds of eras, both Soviet and Imperial. Good place to start would be Robert Conquest's book 'The Great Terror', although a different view, more on the manipulative and secretive side, is Orlando Figes' 'The Whisperers.'

Not everyone who was accused of being (fill in the blank) was killed and/or arrested. Sometimes investigations were thorough and dropped, sometimes they never happened. Try to think of the whole era and situation as reality rather than history. Of the hundreds of millions, several thousands were executed, tens more arrested. A lot, surely, but it's not like it was 50% of the entire population. Now, if you're talking about Georgia in particular, or Chechnya in the late 1940s, then sure, it was like 80%.

In cases in which someone did confess, sometimes torture was used, sometimes heavy interrogations, sometimes confessions were just written up and signed, other times families were threatened - but a lot of times the victim simply signed. It's quite a psychological shock when your God denounces you and accuses you of blasphemy. Many devoted communists were so disoriented and shocked they accepted their fate and wondered at their own faults and shortcomings, certain there must have been some mistake.