The acronym 'MICE' is often used as a summary of four factors which can drive someone to commit espionage:

• Money: pay for information. There are plenty of spies who simply recognised that the Soviet Union would pay for what they knew: Robert Hanssen or Aldrich Ames, for example.
• Ideology: some spies genuinely hold strong political beliefs, and view espionage as a political act. Prime example here is the Cambridge Five, who were spotted and recruited by the NKVD/KGB at university because they were known or suspected communists.
• Coercion: simple blackmail. Many people will go to great lengths to avoid having their dirty laundry aired in public. The KGB was known to set up its own snare operations for this purpose: look at John Vassall, a homosexual British civil servant who was lured into a KGB honeytrap, photographed and then blackmailed into providing information.
• Ego: the hardest to interpret, but essentially the sense of doing something 'big' can appeal to the self-importance, especially of low-level functionaries.

Soviet intelligence officers — like the intelligence officers of any country – used all of the above, and more, to manipulate people into providing information. As /u/abt137 pointed out below, many of their recruits were 'walk-ins' (ie. direct inbound approaches to the KGB).

I'd also second the suggestion that you look at Christopher Andrew & Vasili Mitrokhin's The Sword and the Shield for a great history of Soviet intelligence operations — it's my go-to source for any question about Soviet espionage. Andrew has had unparalleled access to a couple of major Soviet defectors (Mitrokhin and Oleg Gordievsky) so his work on the history and practice of Soviet intelligence operations is unbeaten, to my knowledge.

Believe it or not things were simple, I'd say there were 2 main channels to recruit people:

• Walk-ins. As simple as that, people who would walk into an embassy, not necessarily the Soviet Union one, could be Bulgarian, Polish etc and eventually the Soviet Intelligence services would be alerted. They'd later decide how to handle the person either by themselves or leave to a proxy like any of the Warsaw Pact members. Reasons to walk in would vary but either ideology, disenchantment, revenge and often money are regular reasons; it happens still today.

• Approach. This could be based on a number of reasons, for instance people under strain due to financial and personal issues, classics cases are those having lovers to maintain, gambling debts etc, Soviet agents and moles would spot these persons at risk and approach them or blackmailed them trying to basically force them to work for the Soviet block, I doubt they were ever converted.

Some agents were left from the 30s like the Cambridge ring (Philby et all) who had an ideology reason to convert but after WWII the 2 bullets above would be somehow the main methods in both directions I have to say.

An interesting reading is that of the Mitrokhin archives.

http://www.amazon.co.uk/The-Sword-Shield-Mitrokhin-Archive/dp/147088934X