I chose Kanban after extensive study of ToC. I read The Goal, beyond the goal, the phoenix project and many more. My team (Computer Infrastructure) was the primary constraint of the IT value stream and I needed to correct that. My goal, shift the constraint to business solutions/project side.
2) HOW you did it
I talked. A lot.
Started a test board and asked my team to start inputing their tasks and observe wip limits.
Created a bridge program that sync'd tasks in our ticketing system with columns/teams in our SaaS kanban board.
Instituted daily 15 scrums to discuss the contents of the board and ensure flow.