Well, I just happened to see this (don't get into OT much) and figured I'd respond since I have some experience in this area.
My son had some warning signs early. He would laugh a bit and respond to us in some ways, so we didn't really start to worry until he was 2. He was talking, but it was really hard to understand -- impossible unless you were around him all the time. So we had him evaluated by BabyNet, which was a state program to identify developmental issues in babies and toddlers. They told us our son was fine.
At three he began reading on his own. My brother didn't believe me until he visited and pointed to random words in the newspaper which my son would then read. He always loved books and spent a lot of time with them; of course, we encouraged this. He would also memorize books, tv shows, etc and parrot them back all the time, mostly to himself. We tested him one time and he was able to memorize "The Lamb" by William Blake word-for-word at age three.
We thought he was some kind of genius. Turns out he's high-functioning autistic. Maybe that is some kind of genius, who knows.
When he was 3, nearly turning 4, we started him in kindergarden. After a couple months, his teacher arranged a meeting with us and gently recommended he be tested by a developmental pediatrician due to his memory, etc. Of course, we're no dummies and we asked if she thought he might be autistic and was this part of the reason she wished us to have him tested. She just nodded silently. But she was very kind about it, very understanding. Glad she recommended it since otherwise we might have delayed in getting him tested.
He wasn't engaging with other kids, it was a struggle to maintain eye contact with him, or to keep his attention for any length of time. Other kids would sit in a circle when told, but my son would be unresponsive or else sit for 5 seconds, then wander off. He would only do his own thing (e.g. sit a read) and would not follow instructions or be responsive at all.
It was very strange, because although we did see some hint of these issues at home, for the most part he would play and talk with us.
Of course, it took 9 months to get an appointment since the specialist was overbooked. We didn't want to wait that long, so we asked his regular pediatrician and researched on our own, and got a recommendation to a very good ABA therapist. He wasn't officially diagnosed, so insurance wouldn't cover it, but we went ahead and started therapy.
We also explored "floor time" therapy which is more relaxed and natural than ABA, and is what our son's OT was very fond of. We ended up combining the two by being very involved in our son's ABA and providing suggestions and inputs on what programs to work on, and how they might be most effective. Strict ABA has the therapist working at a table all the time, but we rolled in some "floor time" methods so the therapist would take our son into the playroom to work with him, or outside to kick around ball, etc, while working through some programs (if they were suited to that).
After nine months, he was officially diagnosed as having high-functioning autism. Turns out our insurance still wouldn't cover ABA. We continued with it regardless because it seemed to help, although it was very expensive. In the intervening years, my state passed a law that required insurance to cover ABA. Turns out I'm still not covered because the company I work for is self-insured and not beholden to state law, only federal law. I could talk a long time about this, but will not. Suffice to say, we've paid out a lot for therapy, but fortunately have not had to go into debt since I have a decent paying job.
Long story short, my son is now 9 and is doing pretty well. He talks to us all the time, wants to play with us, loves video games but also plays with legos, magformers, zoobs, has started taking piano lessons and memorizes songs almost immediately. He still likes to read but tends toward books that are too young for him -- he has a fondness for things of his youth; he remembers Blue's Clues, baby books, etc, which are beneath his level, but he is still drawn to them. We have to work with him to read "Magic Treehouse", "Willy Wonka", and other chapter books that are appropriate for his age.
He does a lot better with other kids. He used to ignore them and just play by himself, but now engages other kids successfully and joins in with their play at times. Of course, he still prefers to play by himself, but knows that at school he's supposed to be social. He's great at math, loves geometry and certain sciences.
We still have struggles. The aforementioned juvenilia, perseveration (repeating phrases, typically from books or movies, to himself), sometimes he just seems "spacey". He talks in a kind of sing-song voice that's distracting if you're not used to it. He struggles with reading comprehension in history or literature, which is understandable since you have empathize and understand character motivation.
But we love him. He's our son, and I can't imagine life without him. He started to be able to beat me at some video games, his favorites are puzzle-type games (Meteos, Boom Boom Rocket, Zuma, PvZ, etc). He also loves board games and will memorize the rules word-for-word.
He has learned to ride a bike, which can be a big struggle for autistics -- I almost had him riding when we enrolled him in the iCan Shine camp; they closed the gap expertly and he was independently riding in less than five days. We're still working on swimming, but he loves the water.
I count us and our son lucky for a number of reasons. I tend to look on the bright side most of the time.
All this to say, good luck to all who are dealing with this issue. The spectrum is broad and no two kids are the same, but you can have success.