Don Vito Corleone (MARLON BRANDO) is the powerful head of the Corleone family, which deals in unions and gambling, free from any consequences as enough political and legal power has been bought over the years. On the day of his daughter Connie's (TALIA SHIRE) wedding, we are introduced to all the members of his family, professional and personal. There's Sonny (JAMES CAAN), who is susceptible to bad tempers and is an active member in Vito's circle, becoming more involved after Don Corleone is felled for a time by the bullets of assassins.
Tom Hagen (ROBERT DUVALL) is a consigliere, a trusted advisor to Don Corleone, who was taken in by the family at a young age when it was discovered that he didn't have a family. He grew up, became a lawyer, and makes sure that all that Don Corleone orders is followed and argues against decisions that would be dangerous for the family.
Then there's Michael (AL PACINO), the war hero of the family who has just returned from his time in the war, bringing along with him Kay (DIANE KEATON), and a desire to remain as he is, not to be concerned with the inner workings of the criminal aspect of his family name. But it appears he doesn't have a choice, not only because he bears the Corleone name, but also because of what happens to his father that brings him into that circle, after he's harassed by a police captain and is angered by the incident. But with Michael, it's not an anger to match what Sonny feels when something bothers him. It's more like an anger with a cool, aloof exterior that gradually develops inside, and plans start to form about how to take care of those who have done wrong by him.
There is also Fredo Corleone (JOHN CAZALE), brother to Sonny and Michael, who stays more along the sidelines when we first see him, but grows more involved once it's decided to look at Vegas as a viable prospect for the Corleone business.
Besides the family, there are also those who work for the Corleones, such as Clemenza (RICHARD S. CASTELLANO), who permanently dispatches those who have displeased any member of the family (namely Sonny and Michael), as well as an expert on guns and how to not be fingered as a suspect in any crime. There's also Tessio (ABE VIGODA), another advisor, but with far less pull than Tom, as well as competing heads of New York crime families, such as Don Barzini (RICHARD CONTE), and Philip Tattaglia (VICTOR RENDINA). And the drama builds within all these elements.