Formal Visual Analysis: The Elements & Principles of Composition by Jeremy Glatstein is a very concise explanation. It is worth keeping as a check-list. When looking at work by other artists, we can examine how they use each of these elements and principles in their work. When designing for ourselves, we can make sure that the final design addresses each item on the list in a sensible manner.
In any work of art, all of these elements and principles will be present, but some will be more obvious than others.
For those who want more depth to their understanding of design, Art, Design, and Visual Thinking is an entry level course, an introduction to design concepts and the idea of visual language. If you plan on using color in your work, whether by painting or just using more than one species of wood, Cyndi also mentions an earlier post of hers, Online color training and tools.
Cyndi also recommends a couple of books in her post, but I would also like to add Design!: A Lively Guide to Design Basics for Artists & Craftspeople
which was recommended to me a year or so ago by Bobbi Chukran, and I find it very useful. It covers pretty much the same ground as the online course mentioned above, but has lots of examples and analysis of designs in a wide range of media.