There are few American philosophers better qualified to write on secular humanism than Paul Kurtz, and his What Is Secular Humanism? attests to that fact. This small book, which is actually the text of an article Kurtz wrote for the New Encyclopedia of Unbelief, is a very good primer on the conceptual structure of secular humanism. Perhaps because he's a philosopher, Kurtz doesn't merely offer assertions and descriptions (as other introductory texts on humanism--e.g., Jim Herrick's Humanism: An Introduction--do). Instead, he seeks to provide arguments that defend humanism's basic conclusions.
The substance of Kurtz's argument is the book's second half, "A New Paradigm" (in the first half, he offers a quick look at the history of humanism). According to Kurtz, the humanist paradigm has six main characteristics: (1) a scientific method of inquiry; (2) a naturalistic cosmology; (3) a nontheistic orientation; (4) a commitment to naturalistic ethics; (5) a commitment to democratic forms of governance; and (6) a commitment to international cooperation. It might be argued that several of these characteristics aren't really unique to humanism. But to give Kurtz his due, his point seems to be that the convergence of them all constitutes secular humanism.
In discussing these six characteristics, Kurtz especially shines in his treatment of naturalism and naturalistic ethics. In discussing naturalism, for example, he points out that "nature cannot be reduced simply to its material components; a full account also must deal with the various emergent levels at which matter is organized and functions" (pp. 26-27). In doing so, Kurtz avoids simplistic reductionism. When it comes to his defense of naturalistic ethics, Kurtz summarizes his position of objective relativism, which he elaborated on in his Forbidden Fruit: The Ethics of Secularism (reprint, 2008), and argues that "three key humanist virtues are courage, cognition, and caring--not dependence, ignorance, or insensitivity to the needs of others" (p. 38).
Kurtz concludes his book with an excellent four-page bibliography. All in all, probably the single best short introduction to secular humanism available.