I would assume you would do it by proving that the instances of autism or disabilities that occur directly after immunisation are caused by something else, and it's a coincidence that the child was vaccinated recently.
You would have to show the cause of autism in every child, and even then it wouldn't prove that vaccination does not cause autism, just that in the cases you have examined there are other triggers that could have resulted in the autism.

How to prove that vaccines do not cause autism? Showing that autism may be caused by all these other things doesn't prove that autism can not be caused by vaccination. You may be able to say that there is no evidence of a link between the two, but this still doesn't prove that there is no link.