Nature
Generally, Christian Apologetics is about giving reasons (or philosophical justification) for your faith and/or evidence for the truth of theism and in particular Christian theism. According to 1 Peter 3:15ff, it is about being ready to give a reason for the hope that is with in you, yet with gentleness and reverence. However, it also can be thought of as broader than merely giving justification for Christian beliefs (especially about Jesus), it can also call attention to the relevancy of Christian beliefs especially to a particular audience. Thought about in this way, cultural apologetics would be understood as a part of larger Christian apologetic task of showing justification for the truth of Christian beliefs, but also showing the relevancy of those alleged true beliefs to particular audiences.
We think there is benefit to thinking of it this way as long as you keep clear that cultural apologetics is not to be understood (or practiced) completely apart from general apologetics and the truth claims it intends to justify. One such benefit would be that it may help one focus on cultural apologetic skills and content and focusing on that can produce good things. That is, it can achieve good things if it is able to avoid drifting into thinking that cultural apologetics is all there is to do.
Categorizing the project in this way can make it more clear for the apologist that she is making both truth claims and bringing up relevancy issues in doing this discipline…and as long as they do not get adrift (or let their audience drift) from that unity, there is no harm and no foul. Further, focused study in cultural apologetics can help apologist better understand the importance of cultural analysis in presentations to various audiences, instead of assuming everyone reasons the same way about things or shares the same cultural heritage. This is of particular value in dealing with subcultures like academe that have their own inherited and widely shared interpretation (more vulgarly, “spin”) on the way things are. That is, by focusing on cultural apologetics an apologist can better understand how the dominant ideas in a culture influence the way people think and allow her to bring that to the attention of her audience and at the same time help their audience entertain a different way of looking at things. This job becomes more and more important in western society as it becomes increasingly secularized and because of that secularization, the culture displaces and disenfranchises a Christian way of seeing things.
Skills
What we believe is needed to be effective as a cultural apologist for Christian faith is a facility for understanding the cultural nuances of various audiences, adapting to that without distorting the truth of the gospel, with the intended result that the gospel is better understood and accepted by the audience in a credible way. So communication skills and cultural analysis skills are very important. You will find many resources on this site to help you improve in both these areas.
Examples
Examples of doing (effective) cultural apologetics can be profitably categorized into two main categories: 1) exclusive cultural apologetics and 2) a mix of cultural and justification apologetics. In the former category of the two mentioned, a good representative of it would be Dr. Francis Schaffer. That is, a good deal of his work in apologetics was aimed at what he called “taking off the roof” of competing world views, by showing their cultural inadequacies and especially their existential insufficiency…and showing the existential viability of Christian faith. That is, Schaeffer mainly reasoned with his non-Christian audience that if they consistently followed their own worldviews it would likely produce ways of living that were not viable—that’s not the same as showing Christian faith is true. In the second category mentioned above, Dr. William Lane Craig and Dr. Paul Gould are examples of apologists who by their work both defend the truth claims of Christainity philosohpically and theologically, but also endeavor to show the relevancy of Christian faith in various ways to unbelievers and in ways that are culturally attractive.
Finally, we do not want to ignore the importance that integrating our faith into the academic disciplines is a way to show cultural relevance. Indeed, one of the more persuasive means that metaphysical naturalists can showcase the relevancy of their worldview to the life of the mind is that they have worked long and hard at “naturalizing” the disciplines. They have also worked long and hard at excluding other metaphysical worldviews from being credibly involved in the "the conversation"—especially Christian faith perspectives. Strictly speaking in doing so they do not show that metaphysical naturalism is true—an often misunderstood consequence—they are showing at best, that their metaphysical (or instrumentally understood) ideas have explanatory power and that they have the cultural power of exclusion. Not to make too fine a point of it: explanatory power has tremendous cultural power even when it concedes it has not shown those beliefs correspond to reality. Thinking Christianly about the disciplines at a high level of cultural sophistication could achieve a similar result.