How does autism affect the brain?

No one knows. Autism is defined as a group of symptoms. They probably have many causes. Although there are several good theories and some studies that show brain changes in autistic people at this point no one knows the answer to your question.
Many anatomical . differences on MRI's in brains of people with Autistic Spectrum Disorder vs. those of neurotypical people have been reported, but the Autism Brain Imaging Data Exchange confirmed only 3: larger volume of ventricles (fluid-filled spaces), smaller volume of central segments of the corpus callosum (midline band if nerve fibers) & increased thickness of several areas of the cortex. Citation below.

Related Questions

How does autism affect the brain?

Many different way. Autism causes mild to significant changes to a diverse number brain processing centers. Read more...
It's complicated... Autism spectrum disorder (ASD) is a range of complex neurodevelopment disorders characterized by persistent impairments in social communication, and restrictive, repetitive, and stereotyped patterns of behaviors, interests, or activities. How it affects the brain itself is more complicated. Go to NINDS.NIH.GOV and search: Autism, for more detailed answers. Consult a HealthTap provider as needed. Read more...
Different ways. Typically those with autism have impaired social skills, sometimes poor eye contact, perhaps lanugage or learning problems, stereotypical behavior, repetitive behavior, sometimes sensativities to textures, sounds, tastes, smells, or changes in routine. Autism is a spectrum disorder and some have it severe, some have it very mild, each person is different. Many children also suffer from GI prob. Read more...
Intense research. Autism spectrum disorder is being studied by some of the best laboratories in the world. Molecularly there have been alternations noted in epigenetic areas, and positron emission tomography has revealed alterations in virtually all neurotransmitters. It thus is extraordinarily complex. Read more...