Notes on e. O. Wilson's the meaning of human existence

I am struggling with how evolution works. Wilson seems to be saying in his theory of multilevel selection (eusociality) whereby "hereditary social behavior improves the competitive ability" both within groups and between groups. Which seems to mean that certain behaviors are passed on because they increase an the organisms ability to compete with other organisms with shared Dna (within groups) and non shared DNA. How does ths work given that genes are the unit of natural selection not the organism itself? So I guess that a gene prescribes a trait and the trait can be selected in competition within or between groups. So if the trait is good communication, those who outcompete the other groups within group communication will survive longer. But genes don't act on their own.
There isn't a gene for good communication so how can a gene prescribe a trait? And if it's multiple genes, and culture and rna all involved, how would all of those be selected for good communication? Clearly, I am not getting this.

Wilson adds that competition within groups is what selects for selfishness because you have to compete with one another for resources. But competition between groups increases altruism because you have to cooperate with your group to beat other groups. Creates tension between selfish and unselfish behaviors

One of the better reviews of the book, http://www.independent.co.uk/news/science/why-richard-dawkins-is-no-scientist-the-survival-of-the-least-selfish-and-what-ants-can-tell-us-about-humans-eo-wilson-on-his-new-book-the-meaning-of-human-existence-9849956.html