Am sure you will have lots of replies by time I finish typing this!
We use ABA, we started at 2.10 and my son is now 4.
Applied behaviour analysis is a very structured way of teaching children. It breaks down tasks into their smallest components and teaches them one step at a time. So if you think about learning to swim you might sit on the side and put your legs in, then learn to put your face in the water and blow bubbles, then you might learn how to move your legs and then arms using floats and then gradually work up to actually swimming. ABA does this with everything but into its most tiny steps
So as an eg when we started DS could not copy a simple instruction he would not look or respond when we spoke, so ABA staff found what he liked (they watched what he went for in a room) and then gathered up those things. They then put 2 bricks on a table and said 'give me red brick'- of course he ignored them - so they did it again but this time they put their hand over his and made him give them the brick and then immediately gave him a favourite toy. This way he quickly learnt if I do what they want, I get things I like so he was motivated. We then figured out what he already knew eg colours and what he didn't know.
There is a focus on rewarding behaviour you want to see more of eg speech and ignoring behaviour you don't want eg aggression. So if DS kicks etc he has anything he is playing with taken away and is ignored but if he asks for something spontaneously we give him loads of praise (he no longer needs actual toys) or tokens on a reward board where he earns time to go and do freeplay. They reward behaviour which children with autism find hard eg just looking at the toys (DS would try and build bricks while looking out the side of his eye and using one hand so they would reward him if he looked at the brick and for using 2 hands) and now he builds towers like any other child - although his concentration span is shorter (but improving). Much of it is taught using prompts eg physically prompting and then fading out prompts asap so the child really learns the skill independently and is not reliant on someone to tell them to do it.
Its very systematic so we would teach DS to copy or follow instruction eg clap hands - then we would ask him to do 2 things eg clap hands and sit down and build up. Then do it in different settings and with different people. Then use imitation / instruction for more typical play eg crashing 2 cars together - then adding sound eg he would copy crashing two cars and saying 'crash' - then getting him to copy another child doing it - then starting with 2 step instructions etc So there are heirarchies of teaching skills with it getting harder very gradually. So at the start DS could not copy 1 step, used only 2 words functionally (although he knew 100s) or follow a 1 step instruction but within 6 weeks he was using words to request things, using 2-3 word sentences to request, following long chains of imitations and following longer instructions. It is hard painstaking work for DS (some children make quicker progress some slower) - some things take months to teach others he gets in a day. Its not a cure. But for us its been very effective where other approaches have failed.
ABA staff also take data and evaluate it - so it is a science - so the staff would do the imitation programme say with the cars and score how often he got it right at 1 step then if he got 80% success 4 days in a row they would say he had mastered that skill and then move onto the next mini step. And there are programmes for everything - language, play, brushing teeth, not hitting, sharing etc etc every aspect of life is worked on very systematically.
You can watch some video on youtube and look at websites like Treehouse, PEACH, Autism Partnership.
I actually find it hard to explain ABA really you need to go and see some (we often have other families come and watch DS who are thinking about ABA) and then the penny drops.
Its also supposed to be intensive - anything up to 40 hours a week. We did 15-20 ourselves (with a supervisor training us) for a year until we got to tribunal - and then we won 35 hours a week funded by local authority. LAs hate ABA as its so expensive. It has had a reputation of being harsh (which dates back to when it started when instead of rewards they used punishments) but modern ABA is not it should be very fun and playful but there is an insistence the child do what its asked to get rewards - so this is the behavioural bit as you are very firm and consistent - but actually children with ASD like this clarity. You will still come across very negative views about ABA because of this history (although to be fair all children in those days were subject to corporal punishment). Because its expensive the negatives are perpetuated as a reason for families to be denied ABA eg its very cruel, you drill a child for hours etc etc
DS has his ABA at home and in nursery - so we employ staff who go to mainstream nursery with DS. We hope to keep it into reception and beyond. Before tribunal we had just a mainstream 1:1 and that was hopeless as while they were well meaning they did not have the knowledge of how to teach a child with autism. It was just babysitting. We were denied a place at special school (we would have tried this as really we could not afford ABA for a year we are broke now)
Many children with autism need to be taught things in a structured 1:1 way as they do not learn from watching other children / their environment. However the aim is to teach the 'learning to learn' skills eg paying attention, being in control of their behaviour, being able to imitate etc in the hope that children will become more tuned into their environment and will be able to learn more typically. Some children who do learn how to learn in a more typical way do exceptionally well and can become indistinguishable from their peers. Thats not to say its a cure - more they have learnt enough strategies to be able to adjust.
Many special schools and ASD units will use elements of ABA and there are some ABA schools around the country - but if you want the LA to pay expect a battle - really you have to do it yourself for a while to prove it works for your child - and ideally have tried the LA offering to prove it did not work.
Completely on a different note - many parents recommend Hanen More Than Words book when you get a new dx which has strategies eg especially use of visual supports etc as a good place to start if you want to teach yourself some things to help.