Practice your debating skills. This may seem obvious, but it is crucial. Prepare, both on your own and with your team members. Research your own arguments thoroughly. Anticipate the counter-arguments that the other team is likely to make, and include answers to these, in your own case. Prepare for any questions that are likely to arise and plan your answers. Check that your timing is precise and that you will neither run out of things to say, or rush your last points.
Find out as much as you can about the judges, particularly any foibles, likes or dislikes. Attend other debates and take notes of your impressions of the participants. Work on your style and avoid just trotting out a list of points. Look at the flow of your arguments and check that one point leads neatly to the next. Focus on clarity and do not try to confound your audience with convoluted arguments. Everybody should be able to clearly understand what you are saying.
Consider the ethical dimension of your argument. According to "The Tech," this is something debating teams often overlook. Think laterally, and include an argument that might not be obvious, or may even be counter-intuitive, if it illustrates your case well. Practice your presentation skills, asking a trusted friend to give you an honest opinion.