The Team Leader's role in an search is to guide the team to the successful completion of the task in an effective and efficient manner. This means that although he/she is the leader, all must work together in a common direction, with a common goal. Success includes safety, welfare and even the morale of both the subject and rescuer or emergency worker.
The team will be the most efficient if the Team Leader knows who the people on his/her team are and what they can do. If the Team Leader doesn't know them to start with, he/she must work quickly: find out names and ask questions to assess team members abilities and limitations The Team Leader also needs to know what is available and how to use it.
Communication within the team is vital. Be clear and specific and delegate by name. Delegate individual tasks and ask to be informed when it is complete. If the Team Leader is unsure, he/she should consult your team, but then make the decision. A committee is less effective than a team, so a Team Leader must not abdicate his/her responsibility to make decisions. Debate should be avoided. It doesn't get things done. Sort differences at the debrief and then talk about the problem, not the person.
Morale is important to the smooth, efficient functioning of the team. Don't overstretch the team, or the quality of the job and their safety will deteriorate.
The Team Leader doesn't "do" anything. He/she needs to be able to stand back and take in the big picture, to see how the whole team is going, and to be able to focus his/her attention where it is needed now. A Team Leader that is involved in detail cannot do this.