Scrum is the most popular way of introducing Agility due to its simplicity and flexibility. Because of this popularity, many organizations claim to be “doing Scrum” but aren’t doing anything close to Scrum’s actual definition. Scrum emphasizes empirical feedback, team self management, and striving to build properly tested product increments within short iterations. Doing Scrum as it’s actually defined usually comes into conflict with existing habits at established non-Agile organizations.
Scrum has only three roles: Product Owner, Team, and Scrum Master. These are described in detail by the Scrum Training Series. The responsibilities of the traditional project manager role are split up among these three Scrum roles. Scrum has five meetings: Backlog Grooming (aka Backlog Refinement), Sprint Planning, Daily Scrum (aka 15-minute standup), the Sprint Review Meeting, and the Sprint Retrospective Meeting.
Many books and classes are available from a variety of competing sources of varying accuracy and quality. One place to start would be the Scrum Training Series, which uses an entertaining approach to cover the most popular way of introducing Agile to teams. You can also download the 6-page illustrated Scrum Reference Card.