The University Library's Create Space has lots of materials available for you to use in the space and borrow to use at home. Have a look at the links below to see the material on offer. However, all you really need to get started is paper and something to write with!
DJCAD's Printmaking workshop contains a range of resources to help students experiment with both traditional and modern printmaking techniques. Not listed on their webpage is a Risograph printer. Risograph printers are essentially digital screen printing machines. They work by creating a paper stencil of your image and printing this in layers, a bit like screen printing. They are loved due to the bright colours unique to this kind of printing and imperfect textures that they can produce. They can be a bit fiddly and initially a bit expensive to set up but once you have your stencil in place you can print a large number of copies cheaply.
Outside of the University there are also lots of places around Dundee that might be helpful for finding materials for your zines, learning new techniques or hiring equipment to use. Here are a few independent organisations: