I have been conducting soft skills training for the past few years. I cannot tell you exactly how to begin and proceed as it may vary from person to person. Since you mentioned it is your first soft skills training and it is for team leaders, I can offer a few tips that might be helpful, I believe.
Preparation, Planning, Presentation
If your preparation and planning are good, your presentation is likely to be good as well. So, do prepare and plan well. Don't make the session continuous. Give a break or encourage some fun activity every 20 minutes because most people will lose interest if the speaker continues for a long time without a break.
Make people think that they are thinking, but don't really make them think. People love you only if you make them think that they are thinking, and not if you really make them think. I mean, shoot them a few questions that would be easy for them to answer so that they'll feel they know something. If you ask questions they can't answer, they may feel slightly embarrassed. If your questions are a bit tough and you feel they may not be able to answer them, then go ahead with the answer.
Since the audience are already team leaders, they may think they are already leaders and know what leadership is practically. Make sure you honor their pride. So, don't always teach them 'How to win?' Instead, make them think 'Why it fails?' Then come up with how to overcome it.
Since the audience is only about 10 members, the trainer may lose interest. And you said it is your first training session, so for you, the small crowd will be easy to handle. A small crowd is better for beginners. Don't worry about it.
I don't know about your rapport with your audience. A friendly trainer will be more preferred than a professional hostile trainer by any audience. Make the people feel that you are friendly and the session is fun-filled. Keep your voice pitch and loudness the same from beginning to end. I mean, don't lose your energy level. Only then the program will be enthralling and the audience will not get bored.
Make the session interactive. Before you make a point, get the ideas from the audience and discuss them. If they have missed anything, then add and summarize your points. By this, you'll make them feel that you are not telling them what they already know.
Many other things can be said, but I believe this is enough for the first training session. My post may be late for you as it is Friday. All the best if I'm not late.
Regards,
Rajaguru
PeakPro Solutions, Chennai