A Neuropsychologist will usually administer several standard tests. At this age the tests are very unreliable. There are other signs of behavior they looks for.
Admittedly, we went into it thinking "maybe it's Autism, maybe it's not... but we can't get therapy for the delays unless we get the diagnosis". Having read substantially more and seen more children on the spectrum it's pretty clear. But it's a good question and by no means an exact science.
I recall a study that was done on early intervention (12 months I believe) where the majority of children diagnosed with Autism were able to shed their diagnosis by age 3 (or something like that). The trouble is that the initial diagnosis may have just been wrong... it may have just been a delay caused by something else. The good thing is that the therapy is beneficial for anyone... so there's little need (beyond monetarily) to be concerned with misdiagnosis.
There are some tell-tale signs to be aware of in children or infants. Lack of speech, lack of eye contact, non-reactive to environment (seems deaf), no pointing. Repetitive behaviors and obsessions/compulsions can start to show early as well. Even things like toe-walking are very common (though toe-walking isn't exclusive to autism, but can be an indicator).
More promising on young children than tricky psychological evaluations, a professor at my university has shown that there are ways to diagnose autism from structural differences in the brain using MRI images and image processing techniques.
