I think to a large degree they can be learned, absent any pathological condition that interferes with this sort of learning, for example, autism, which often creates a deficiency of empathy, thus making people skills difficult or impossible to acquire.
In my opinion, people skills are best taught with modeling, practice, and critique. These are largely communication skills, and if those cannot be taught, we have all wasted a great deal of time, money, and energy offering communications courses and degrees. They are also a form of emotional intelligence, something that therapists help people with every day.
People are capable of observing successful transactions among others, and they can be taught to analyze what makes those transactions successful. They can then practice those behaviors and with repetition and constructive criticism, internalize them. Sometimes there is a behavioral aspect to this, too, with negative and positive reinforcement helping us to make corrections.
Think about this for a moment. How do any of us learn any people skills otherwise? We learn by observing our parents and siblings, interacting with them, practicing what we see, getting some criticism and then making corrections. There are behavioral aspects here, too, with the consequences of behaving appropriately or inappropriately.
Though individuals have different aptitudes for picking up "people skills" through natural interactions and observational learning, all can learn through direct instruction, practice, and feedback. Individuals with social skills deficits, such as those diagnosed with autism, often benefit from social skills groups, role playing, social stories, and direct feedback. Often there are unwritten rules for social interactions that, once understood, can demystify interacting with other people and make the individual more relaxed and confident when conversing with individuals. Being able to read body language and facial expressions, tone of voice, and sarcasm or veiled language all become important. Nonverbal cues are often missed by individuals with "poor people skills" until explicitly pointed out, as in letting the person know that s/he is violating the cultural norm of personal space or not making sufficient eye contact.
Group dynamics are a more complicated matter, especially when people behave in ways that they typically wouldn't if it were not for the group's presence. Managing one's reputation, avoiding being the target of a group's gossip or bullying, and "working the room" to persuade or win people over to one's side are concerns that become more prominent in the teenage years and in the workplace. Again, these are skills that can be learned, though the situations can be more volatile - it's difficult to predict all of the behaviors, interactions, and perceptions of all the people in a group, and there may be others in the group acting as competitors or adversaries.
Underlying all social skills is self-regulation and awareness of one's own emotions. An individual with a volatile temper, who is easily irritated and annoyed by others, might have a difficult time maintaining a calm demeanor in social interactions, and might offend without really meaning to. An individual who is feeling extremely anxious or depressed may need to take care of the underlying mood issues so as to be fully available and present in the social interaction, and not overlay the interaction with interpretations or fears that detract from accurately experiencing the other person's intentions.