This title is on purpose a bit misleading because writing a good paper is not really an art provided that you have quality results from your research. Getting such results however may be compared to art. I would instead say that writing a paper is a craft and that it is best learnt through practise.
Here are some tips that I have picked up over the years after having been involved in writing more than a hundred and fifty papers, having been a reviewer for several journals, and after some years of being an associate editor of an international journal. The most important parts to focus on are the abstract, the introduction, and the conclusion. The rest of the paper is then more or less given by your material and therefore it is not covered here.
The abstract is often written after everything else has been completed. Unfortunately, by the time you get to it, you may be so fed up with your paper that the quality will suffer. This is a pity as the abstract is usually read by many more people than the rest of the paper.
The paper by professor geology Kenneth K. Landes (Univ. Michigan) "A scrutiny of the abstract" (first issue from 1951) has some very good points. Notice in particular the examples of a poor abstract initially and how it has been improved at the bottom of the page.
The introduction is second only to the abstract in marketing the paper for potential readers. Its purpose is therefore to tell the reader why he should use time on reading your paper rather than someone else's.
Usually the introduction has three parts:
- A review with status in the field.
- A claim which tells a reader what is new in this paper.
- An agenda which briefly tells the reader how the paper is structured.
Part (2) is where you say something about why this paper is an interesting extension of the historical review in (1). Therefore it is the most important part of the introduction. Read more about this in "A scrutiny of the introduction" by professor of geophysics Jon Claerbout (Stanford). His paper was inspired by Lande's paper about the abstract.
Jonathan Shewchuk (Berkeley) also has some good tips in "Three Sins of Authors in Computer Science and Math". When it comes to the introduction he warns against using obvious and meaningless sentences like "In recent years, the study of ... has become important", and rather get to the point.
The other sin is that the agenda (3) is just a simple table of contents. It can be done much better. Also, there is no need to mention that the paper will end with a conclusion.
Many readers are like me and first look briefly through the introduction and then the conclusion in order to figure out if the paper is worth reading. The last sin that Shewchuk focuses on is to write a conclusion which is not a conclusion, but rather fits better in somewhere in the introduction. Instead, the conclusion should be readable in its own right, it shall give insight into what new the paper has contributed, and it should look ahead and give perspectives.
I end here and want to wish you best of luck with your next paper!