Applied Behavioural Analysis.
Sometimes known as Lovaas Therapy, though some people think LT involves electric shocks (it doesn't).
Based on positive reinforcement of good or desired behaviours.
Desired behaviours (from things as simple as clapping to things as complex as reading/talking/writing etc) are broken down into tiny steps and each step is taught and added to the step before, until you get the behaviour you want.
Each step, or combination of steps, is rewarded by something the child finds rewarding. If a step is asked for and not done it is answered with a "No" (unemotional so danger of upsetting child is minimised).
The steps are entirely based on the abilities of the individual child. Generally a team of people work with a child and includes a Supervisor and Consultant.
In my day the Consultant was invariably flown over from USA at huge cost to the family.
Some therapists charged outrageous amounts per hour, and some families are desperate enough to pay them. Local authorities used to pay therapists £6 an hour, so the family had to find the extra themselves. A lot of the families I used to work with had taken out second and third mortgages to pay for their child's therapy. It infuriated me that they had to, as if they didn't have enough to cope with as it was.
No idea if things have changed in the last 15 years.
The therapy worked with most autistic children by the way. I only knew of one who didn't respond well, and it turned out he wasn't autistic, but had even worse, more complicated, problems.