Most Agilists will agree that the two best ways for small teams to become self-organizing is either Kanban or Scrum. When to choose one over the other is not always clear, so there are some guidelines below. Note that almost any team can implement Kanban and see improvement in their work. In fact, even Scrum teams use Kanban to visualize the work they take on in a Sprint. But Scrum has benefits that do not exist in Kanban, so it's often good to implement Scrum whenever Scrum is possible. Here are some Guidelines for When to Apply Scrum over Kanban:
Team is focused on creating one particular product or outcome as a result of the team's efforts. In other words, everyone is working on the same thing. Often, everyone working together on the same product is a good indicator that the team should use Scrum over Kanban. Kanban can be used when different team members are working on different products and there is little need for collaboration between all team members. Customer support and operations are often good candidates for Kanban and horrible candidates for Scrum. The Scrum team should be focused on one combined output.
Planning horizon is one week or more. In other words, the team can plan what it's going to be working on for at least the next week forward. In order to use Scrum effectively, the team needs to be able to plan out the Sprint. Since a Sprint is minimally one week long, the team needs to be able to plan its combined activities for the week following the Sprint Planning event. If a team's priorities change on a daily or hourly basis (such as customer support or operations), Scrum is not a desirable method of self-organizing.
Given 1 and 2 above, if the team is young or not experienced with working together, Scrum is is a good solution. The rigor of Scrum enforces a planning process that helps young teams collaborate in a way that Kanban does not achieve. Young or inexperienced teams benefit from this rigor. Teams that have been working together for a long time may abandon some of the rituals of Scrum over time and revert to Kanban, but young teams that are learning to work together will benefit from Scrum.
Many teams will have heard of Scrum as the best way to become Agile but then find it difficult to organize into a Scrum team. Often, changing priorities or having too many different products to work (items 1 and 2 above) on will cause these problems. That's when you know that your team may benefit from the less rigorous approach of Kanban. Kanban is also an easier sell to skeptics. Since it requires little initial effort or change, people are less opposed to it. As the team sees the benefits that Kanban brings, everyone starts to appreciate it, even the skeptics. So, another indicator for Kanban is resistance to organizational change. Please see my LinkedIn Article on this subject.