All you really need to make a zine is something to say, paper and a pen, and access to a photocopier so that you can get your message out in multiples.
It’s also nice to have a stapler or a needle and thread to hold the pages together. Sharpie markers, glue sticks, scissors, and old magazines and catalogs to cut up are good to have on hand, too.
You can handwrite your zine, type it on a typewriter, write it on a computer, make words with alphabet stamps or cut letters ourof magazines.
Here's a pdf that shows you how to make a 6-page (+ covers!) mini zine out of one sheet of photocopier paper.
The Life Magazine Archive in Google Books is an excellent source for vintage photographs and advertisements from 1936-1972. You can download the magazine cover thumbnails as jpgs (perfect zine size!) and take screen shots of any internal content.