Using your research into artists’ books and fanzines as a starting point, think about their physical or design qualities, and creatively apply some of these approaches to your own designs.
For example, there’s a distinctive visual quality to many fanzines which comes from a ‘cut and paste’ approach to designing and through the use of cheap photocopying and printing. Punk fanzines in particular make a virtue out of having limited resources, no computers and little, or no, formal training as graphic designers. Use your sketchbooks to experiment with a similar ‘cut and paste’ approach by cutting and collaging magazines and other material. What does this approach offer you as a book designer?
Alternatively, you can find other ideas you would like to test out in your sketchbook. You don’t need to make any finished designs, just give yourself room to experiment and try things out.
I’ve decided to have a go at the punk DIY aesthetic that you might find in a zine like Sniffin’ Glue.

Sniffin’ Glue utilises a simple no thrills approach to zine design. The text is handwritten with a marker pen and cut and paste techniques are used for the images.

I cut out some text and images from an issue of Private Eye and created a montage with marker pen added. I thought that the mixture of typefaces created a punk irrelevance and DIY aesthetic. To make it more gritty and consistent I made a black and white photocopy.

I think this black and white version looks a lot better and it evokes the production values that authentic punk zines had where they would photocopy zines in this manner.
Creating something with these hand-drawn and cut and paste techniques was really liberating and makes zine creation accessible to anybody regardless of design skills, which is very in line with the punk spirit.