Start by checking with a teacher or academic advisor. It is important that you have permission from someone at school before you start your book club. Schools have rules that govern student clubs and you'll want to make sure your club is legitimate. Don't worry that you will be turned down when you ask them to help you--your teacher or advisor will be impressed with your initiative, and you'll find them very helpful in the process of setting everything up.
Decide on the type of book club you will start. Fiction or non fiction? Or perhaps science fiction? Maybe you'll want to use your book club to explore the classics. You might find it best to establish a very general book club rather than narrowing the focus to just one genre. No need to limit yourselves!
Get students to join the club. It will be easier to plan your book club's goals and establish the book club's practices when you have a core group of members to help you plan. Start with a few close friends or ask your teacher or advisor to suggest some students they think might enjoy the book club.
Chart a course for your book club. Once you have at least three or four members in your book club, you can establish your club's general course. You and your fellow club members can establish a meeting schedule and a meeting place, decide on books that you will explore together and decide on the best ways to make the book club a fun group to be a part of.
Increase your book club membership. Once you and the other core group members have established the book club, you can start publicizing your club and encouraging more people to join.