The Kanban Clinic

The Kanban Clinic is a place to learn how to get started with Kanban and to learn more about it. The benefits of Kanban over other agile methods such as Scrum include:

The ability to do agile when teams are difficult to form due to certain people being in very high demand.
The ability to control your rate of transition.
If your teams are overwhelmed with work, the ability to determine what the root cause of the overwork is.
Getting more insights into the principles of software development.
Much faster learning than typically achieved with other methods.

Getting started

See Demystifying Kanban: Understanding Its Many Faces for a full introduction to Kanban (or read Demystifying Kanban for a comparable overview). If you are new to agile as well, you might prefer to watch An Introduction to Kanban as an Overview of Agile.

Or watch a couple of excerpts:

Real Tenets of Lean: Avoid Creating Waste By Eliminating Delay. Lean is not really about eliminating waste - it's about not creating it in the first place.
n excerpt Mapping a Value Stream to a Kanban Board. The process of mapping a value stream to a Kanban board and why both are important in improving business-driven software development.

Acceptance Test-Driven Development. ATDD is one of the best returns on investments we know.The benefits are:

significantly less rework of code
higher code quality (many fewer bugs - we've had clients reduce bugs by 92% just doing this)
greater productivity as a result of the higher teamwork and greater quality
faster regression testing

It accomplishes this by:

having better conversations with customers/BAs, developers and testers about what is needed
generating better documentation of the requirements (test specifications add essential clarity)
providing a platform for automating acceptance tests

More information on ATDD:

Load Balancing Strategies for Kanban Teams