Guide to making a 'zine
Step 1: Write your stuff
This is the most important part. If your content isn't interesting, nobody will care how cool your 'zine may look. Make sure your 'zine makes people think and opens their eyes.
Step 2: Layout
You can use whatever software you happen to have, Microsoft Word will do. Publisher is better for making the layout precise by page, but use whatever you have. Unlike the content in step 1, your layout isn't that important. For your first issue, you shouldn't try to make your 'zine too long, generally 1 or 2 pages is enough for the first one. If you want to have more, put it in issue 2.
Step 3: Printing
You're gonna need a printer for this one. Print in high quality, and make a double-sided page (page 2 on the back of page 1). Then, run to the nearest place that can make photocopies. Ask them to make the copies also double-sided, so that it will work out cheaper and easier (no lost pages or staples).
Step 4: Distribution
This depends on your school. If you're just starting out, you can walk around with a pack of issues and hand it out to random people in the hallways. If you get to class early, put one on each desk (again, that depends on your teacher). You could put a pack in a good place, like in the front of the school, or on a table in a hallway. You could also put a copy on students' cars in the parking lot, depending on how your school is set up. Either way, as long as distributing your 'zine doesn't cause much disruption of normal classes, they can't stop you from continuing.