Studying the elements and principles of design is at the minimum a one semester introduction when getting an art degree. However ... it's something artists work on their whole careers. There's always a new way to tweak the lines one is using or how you approach value, color, or texture. A lot like learning how to put the alphabet together into words allows you to begin writing and reading - and then you can spend your whole life learning about and experimenting with the written word!
I like this site from the University of Saskatchewan as a good introduction to design theory. It will take you through the different elements and principles and has good examples.
Then you might want to look at Western Illinois University's page on design to see how artists can push the limits. Their page on Illusion of Depth is especially good.
These pages from the the Getty Museum on Elements of Art and Principles of Design also have a lot of good information and include worksheets to do some practicing. They're designed for teachers to use with their classes, for any teachers out there.
And finally, for just pure fun, take a look at this You Tube video on the elements of art by Maria Maldanado. It made me wish I was still teaching middle school art - what a hook!
Happy Creating! Deborah