Familiarize yourself with the proposition and the arguments for and against it. Assess the depth of knowledge shown by each side. Look for evidence that the speakers have carried out appropriate research, not only into his side's argument, but also the other viewpoint. Ask yourself whether each speaker has the level of knowledge about the topic you would expect, bearing in mind the age and grade-level of the participants if it's a school debate.
Assess the participants' level of confidence. Though some nerves are understandable, the participants should be able to present their arguments in a coherent and audible way. They should not rush through the delivery and should make eye contact with the audience at appropriate times. They should seem familiar with the rules of debate and should speak for the required length of time. Look for coherence in their arguments; they should not just present a series of unconnected points.
Observe the participants' ability to deal with opposing arguments and questions. They should not become flustered or defensive, or take any challenge as a personal criticism. They should show by their answers that they have already thought of these opposing points and, if debating as part of a group, discussed them with their team members. They should be able to address questions in a calm and intelligent fashion.
Apply the rules and any given criteria to your critique. If using a point-scoring system, familiarize yourself with it in advance of the debate and apply it fairly. Make all comments constructive, always starting and ending on a positive note.