I'm very sceptical of Freud and psychoanalysis
There is an ancient and noble tradition of burning a straw-Freud, which started during the Freudian analysis vs Jungian analysis and analysis vs behaviorism conflicts decades ago, and it is still used today to signal your allegiance to a specific tribe, usually either skeptical or religious, depending on context. On LW this tradition is honored during the winter solstice, too.
I would recommend against classical Freudian psychoanalysis in this case simply because it was developed for dealing with stuff like this, which is fairly uncommon in our society; and is probably completely unrelated to autism.
I'm sorry I can't give you a more specific advice than this: try to contact families with similar problems and ask what worked for them. Seems to me that no therapy is scientifically proved yet, but I would probably bet on something like CBT.
When dealing with an autistic child, my impression from reading some blogs is that you should not expect any "common sense" at people-related things. Just accept that the autistic child has greater inferetial distances and problem understanding metaphors, therefore explain to them everything very simply and literally.
Seems to me that no therapy is scientifically proved yet, but I would probably bet on something like CBT.
I assume by "scientifically proved" you mean well supported by the available evidence, in which case CBT has already attained that [edit: I don't mean specifically for autism; Villiam_Bur's comment leads me to infer that he's referring to CBT being a potentially useful therapy more generally]. And the reason Freud is so disparaged is because his methodology was at best proto-scientific and at worst speculation, and yet people still take him seriously. For that reason, I speculate the hostility ostensibly directed towards Freud is actually intended for his current supporters.
First, a short personal note to make you understand why this is important to me. To make a long story short, the son of a friend has some atypical form of autism and language troubles. And that kid matters a lot to me, so I want to become stronger in helping him, to be able to better interact with him and help him overcome his troubles.
But I don't know much about psychology. I'm a computer scientist, with a general background of maths and physics. I'm kind of a nerd, social skills aren't my strength. I did read some of the basic books advised on Less Wrong, like Cialdini, Wright or Wiseman, but those just give me a very small background on which to build.
And psychology in general, autism/language troubles in particular, are fields in which there is a lot of pseudo-science. I'm very sceptical of Freud and psychoanalysis, for example, which I consider (but maybe I am wrong?) to be more like alchemy than like chemistry. There are a lot of mysticism and sect-like gurus related to autism, too.
So I'm bit unsure on how from my position of having a general scientific and rationality background I can dive into a completely unrelated field. Research papers are probably above my current level in psychology, so I think books (textbooks or popular science) are the way to go. But how to find which books on the hundreds that were written on the topic I should buy and read? Books that are evidence-based science, not pseudo-science, I mean. What is a general method to select which books to start in a field you don't really know? I would welcome any advise from the community.
Disclaimer: this is a personal "call for help", but since I think the answers/advices may matter outside my own personal case, I hope you don't mind.