I am having a hard time identifying different principles of design in action. It is hard for me to identify the relationship between different elements on a page and to know what approach was used to create that particular relationship.
How can I identify and understand which principles were used in a design?
I think this is totally normal when you are new at graphic design. Our brain can only hold so much at once, and with practice we are better able to group concepts and notions together as a whole. Another issue that I think is common in our profession is that we often have an intuitive grasp of principles and how to do something (procedural knowledge) but lack a true understanding of what brings these principles to life (declarative knowledge).
To make things worse, graphic design teachers themselves often aren’t trained in pedagogy and this may show in their feedback (e.g. “These colors work really well together!” while gratifying is sort of vague and not particularly helpful if you don’t see what they see. Being able to word it more precisely (e.g. “This triadic harmony is completely relevant with the topic of water and the proportion of each color you’ve used really helps to bring out these important accented parts.“) takes more time and mental effort to formulate and goes above know-how or procedural knowledge of graphic design. Don’t hesitate to ask your teacher if they can be more precise as to why something work/doesn’t work, you may greatly benefit from it!
My advice to you would be to try to build your declarative knowledge of design principles alongside working with these principles and increasing your know-how. Read about them and what they consist of. In parallel, deconstruct the work you do. For example, when you feel something is wrong in one of your works, take the time to go through each principle and check what could be improved.
There are many good books about design principles out there but one that I’ve read cover to cover and has helped me tremendously is Art and Visual Perception: A Psychology of the Creative Eye by Rudolf Arnheim. Although it’s more oriented towards visual arts in general, it explains the underlying principles of how we see what we see. The improvement in my work as I was reading the book was almost surreal. It is a tough read for a non-native speaker but I really recommend at least giving it a shot.