Psycholinguistics is the study of how people understand language. It can cover a number of fields, and provide important insights into our understanding of language.
B.F.Skinner's Verbal Behavior represents a conceptual, theoretical extension of his powerful inductive approach innovated with lower organisms. This approach posits that language, or what Skinner calls Verbal Behavior, is best explored in terms of functional relationships.
This view represents a view opposed to the traditional hypothetico-deductive approachs to language that are largely driven by speculative theories and not integrative, data-driven theories.
Skinner's view of Verbal Behavior was widely viewed to have been "demolished" by Noam Chomsky's critique. However, astute readers will have noted that little of what Chomsky said actually applied to Skinner's work. See, for example, Ken Maccorquodale's On Chomsky's Review of Skinner's Verbal Behavior (http://www.behavior.org/computer-modeling/maccorquodale/maccorquodale1.cfm) for a general statement of the widely held perception that Chomsky said almost nothing about Skinner's work.
Skinner's inductively driven conceptual extension to human verbal behavior has seen an enormous resurgence in applied settings in the treatment of autistic children who were considered "untreatable" by normal approachs.
Skinner's position is that human verbal behavior is, like other behavior, driven by the four-term contingency analysis discovered and refined in laboratory work: one or more motivating operations (MO), one or more discriminative stimuli (Sd), one or more responses (R), and one or more reinforcing stimuli (Sr) make up the four term contingency. Human verbal behavior is analyzable in this functional context.
Children, then, learn language as a function of thousands of instances of verbal prompting, shaping and reinforcement.
Grammar is universal in the sense that the world is universal. The same speakers in all of the world deal with the same world and so speak about it in similar ways. Human language is too young to be a part of the human genetic endowment.