THIS IS YOUR BABY.
As EIC, this book is your baby. It takes 3 months to plan for, 9 months to develop, and only a few days to share with the world once it arrives. It is your pride and joy, and every single page of this yearbook you will have touched and edited by the time it comes out. When I was EIC, I took the utmost pride in how my book turned out. I did not let anyone except for myself put pages into proof and preflight, I had total control over all design elements and spread design, and when people did not do their work (which is inevitable) I took it upon myself to do so. Not everyone who takes the class will care as much about this book as you do, that's just the nature of the beast, but what you can do is show them how much it means to you and then maybe, just maybe, they will feel as though they don't want to let you down. For this is your freedom, I designed every club, sport, people, and baby ad page. I may have gone to the extreme, but I did what I had to do to get the book published with my high expectations of myself and of this publication. If someone does not do their part, it is your job. At the end of the day, you are in charge, and it is your responsibility to know anything and everything concerning every single person in the school and every single pica on each spread. You need to know who is doing what and when they are getting it done, and then ultimately, if it isn't done, you need to be aware that you need to do it yourself. If no one can cover the football game that has to be dom, congratulations! You're now covering it.
That being said...
There are certain responsibilities that you have as EIC. You are largely responsible for designing and gathering whatever content for the cover, endsheets, opening, title page, closing, and parting page. You are also responsible for making sure that everything is done the way that you want. If you have editors that you trust 100% with their work and once they say it is good to go then you send it, that's great! Me personally however, I always check over everything one more time. Ultimately the goal is to win a Pacemaker with every book, and I always have that mentality. Checking something one more time will never be a bad thing.
TEACHING AND HELPING
You should not count on or use class time to do your personal work. Class time should be used for instruction and for managing everyone and making sure that things are getting done. During a lot of this time, make sure and help teach people design who are interested, and instead of leaving sticky notes on people's spreads, go talk to them and explain why and how they can fix it. Never tell people the answers, just ask them questions to help them figure it out on their own. Take the time to teach them the right way to do things, and then you will have less to check and redo before each deadline.