Of all the things that a management can do to help your people become more effective this is probably the area where you will be most comfortable. Management, after all, usually defines the organizational structure of their people.

There is a twist with Agile though. The unit of execution for Agile is not a person (or a full time equivalent or FTE). Instead it is a small Team where small is defined as “less than 10 people”. Steve Denning in his blog post "Explaining Agile" calls this “The Law of the Small Team”:

The first universal characteristic of Agile organizations is the Law of the Small Team … work should in principle be done in small autonomous cross-functional teams …

This is not done by simply dividing up people into groups of 10 (say) but rather requires some careful consideration:

• Cross-functional: Cross-functional means that this Team is constructed in such a way that they have, in most cases, all the skills needed to take a requirement from the customer and get it delivered.
• Soft-skills: In addition to hard skills such as expertise in a particular area, Team makeup needs careful consideration. After all these people will be working together for a long time and if they really are to improve then they need to be able to work together effectively.

In the end, these soft skills are probably the most important requirement for a successful Team as Team members can usually develop hard skills. From recent research at Google:

“As the researchers studied the groups, however, they noticed two behaviors that all the good teams generally shared. First, on the good teams, members spoke in roughly the same proportion … Second, … they were skilled at intuiting how others felt based on their tone of voice, their expressions and other nonverbal cues. ”

Note: although not necessary, typically Teams identify some special roles to help control the flow of work:

• Someone is usually made responsible to defining and prioritizing the requirements (i.e. “what” the customer wants). In Agile implementation this role is often called the “Product Owner”.
• Someone is usually made responsible for helping the Team improve (i.e. the “how” a Team works together). In Agile implementations this role is often called the “Scrum Master” or “Facilitator”.

Creating Teams in this way does not need to go through a “reorganization” process. You can start by creating virtual Teams with clear roles. Over time you might want to consider more formal structuring but it is not necessary to get started.