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This thought came into mind when I was reading Points of view: Elements of visual style.
While there are a lot of questions on software and strategies to make and edit figures, I am more curious about what are the things to consider (design rules) while laying out figures. Factors that come to mind include typography, color template, and proportion.
There are many books on this subject, as Peter Jansson points out, as it is something of an Art/Science in its own right.
However, if you don't feel like buying and reading one or more books on the subject, here are a few basic things that I consider both important, and easy to follow:
Consistency: While people can generally argue for hours over the merits of one colour scheme over the other, what is more important is that you use a consistent one for all your figures. Same goes for fonts and line styles. Also, if you're going to use blue squares to represent some thing in a figure, be sure to use blue squares for nothing else throughout your entire paper.
Conciseness: Try to reduce each figure to making a single point, i.e. try to think in terms of "what is this figure trying to say". It's tempting to pack more and more data into a single figure, but in the end this will usually dilute the message. One figure, one statement.
Clarity: Once you've decided what it is that your figure will say, remove anything from it that does not contribute to this single statement. E.g. do you really need every data point/curve you've drawn? If your statement refers to part of a flow chart or class diagram, do you really need all the other, less relevant boxes/labels/methods there too? Also, if the salient feature of your figure is not immediately clear, don't shy away from adding an arrow or something to highlight it.
Completeness: Holding the balance to clarity's minimalism, make sure there is also nothing missing from the figure which is needed for the statement you want to make. Figure axes labels are a favourite.
Funny how they all start with "C". This is not intentional.
There are many aspects of designing figures/illustrations that are covered extremely well by the books written by Edward Tufte. I would strongly recommend his The Visual Display of Quantitative Information as a starting point.
Some basic notions are to strive for simplicity and clarity. This may seem very obvious but there are many pitfalls and Tufte provides good examples and ways to think about even simple graphics. Design issues such as fonts, line weight, color etc. and thinking about what it is that should be conveyed in a graphic helps to understand how to design efficient graphics. There is a defintion of graphical excellence by Tufte that says that an illustration that provides the reader with as many thoughts as possible in as short a time as possible by using as little ink as possible consitutes such excellence.
Obviously it is impossible to provide a full answer here particularly since it would repeat what is already in print. My personal view is that the book mentioned above is a good foundation to start critically view and discuss illustrations you encounter. Discussing with peers can be very useful. At the same time there is also much tradition in graphics so new ideas may not necessarily fall into fertile soil rigt away.
I rather like the framework presented by Dan Roam in "The Back of a Napkin" as a guide for S (simple/elaborate) Q (quality/quantity) V (vision/execution) I (individual/comparison) Δ (change/as-is) and the who/what (portrait), how much(chart), where (map), when (timeline), how (flowchart), why (plot).
In general, these two dimensions (technically 3 dimensions but some aren't used) are presented in a matrix to demonstrate the basic forms of diagrams you can use for communicating concepts. The book is a little more high-level than many books on this topic for scientific presentation but I think it's important to be able to select the right picture for your message.
Once you get down to nitty-gritty details, then Justin Zobel's "Writing for Computer Science" has a number of really good specific pieces of advice for how to lay out diagrams and tables, including how to typeset them so that people remember how to find them and how to make it so that tables don't look all crowded. The book's title says "computer science" but much of the advice is reasonably general to most quantitative research fields.
Tufte has been mentioned already, but since you're asking for principles, this one deserves to be emphasized:
Maximize the ratio of data-ink to total ink That is, remove anything that doesn't express data, or look for clever ways to make things express data.
Here's an example:
The standard bar chart from any plotting program has a thick border around it and usually some kind of grid. Here, the border has been removed, since it doesn't express any data, and the grid has not only been removed: Tufte has actually managed to express a grid, by removing ink.
The manual for the TikZ LaTeX package contains a very good, 6.5-page section with very reasonable (tool-independent) guidelines (and examples). Just to whet your appetite (and give an idea about the kind of advice contained there, and also to make this answer usable by itself – though please do read the linked document, there's much more to it than what I quote below!) let me quote the list of subsections and short quotations.
