The first thing I do is filter out the tantrums from the meltdowns. I look at the root cause and if it's just a tantrum I switch into "parenting" mode and handle it like I would for my other kid, using discipline and structure to work on eliminating undesirable and changeable behaviour. If it's a clear sensory overload or something else I'd call a meltdown then I do my best to remove the triggers, isolate and soothe her, and get her back to a good place. Then, depending on the situation perhaps try to gently reintroduce the trigger in a controlled manner if I think she can handle it and doing so might help desensitize her to it in the future.

Learning to properly differentiate tantrums and meltdowns and classifying them accordingly was a major breakthrough that really helped me relate to her better and has led to a general improvement in her day to day behaviour.

I try to use what they call respectful parenting. I rarely deal with tantrums anymore. It helps to repeat what they say if they're verbal, and to empathize with their feelings. It really helps if you see the signs. Obviously when trying to take control over them you can expect it to worsen. Giving them choices, picking our battles and asking ourselves will it hurt if he eats his ice cream before dinner can all help. Then being physically active, hydrated, full tummy and rest when needed also helps. It all depends on what they're feeling and going through at the time.

My 9 yr old son and I have a little routine. When I see he is starting to get upset, or already there, first I tell him we're going to breathe. We begin slow, deep breaths in thru the nose and out of the mouth, and make eye contact as much as possible. Sometimes we hold hands or hug and always do it together so he has an example to follow. We do this as long as it takes for him to calm down; there is no set limit, just that there's always a minimum of three breaths to start. We've been doing this very successfully for about three years now, and doing it with him helps to calm both of us down so that when it is time to talk, any urge to raise my voice has dissipated and I am able to whisper explanation and corrections, and he can be receptive to what I'm saying. Now when I tell him to breathe he knows that it means time to calm down and listen, so for the smaller things we only need a few quick breaths in a few seconds before he's ready to listen. This has become a great exercise not just for him, but my non-autistic nieces as well!

Without technicalities...

This is a family member who requires special intimate care. Try your best not to directly offend (taking something from him that he is embroiled in) is a good way to offend!
Pay CLOSE (did I shout that loud enough) attention to him at all times. This child needs your attention, whether it is intimate, or just listening, watching, and taking mental notes.
At one time, when I had heard my grandson needed 4 ADULTS to restrain him for a haircut, the next opportunity I offered to do the honors. First, I kept out of his "zone", his "safe area". I reached in with the buzzing clippers, and allowed him to touch them. Once his curiosity was aroused, he explored further. He knew what it was for; he placed the clippers on his forehead- then pushed the clippers upward. He actually took the first cut himself.
I cut what he was comfortable with; I stopped when he let me know he was done. Instead of fighting with him, I backed off. He allowed me to finish, but I think that was over a period of four days.

Unlike many of us, hair styling is not a strong streak for these children. If he could wait, I could wait.
What I did NOT want to do is create trauma. I do not know what he thinks at any time, I can only hazard a guess.

Overall our time with him was rather "tantrum-free". He had his periods where he would run back and forth down the hall, with a loud hum to accompany him. Other times, a happy-sounding squeal, accompanied by some laughter. He enjoyed studying and testing plastic straws for tensile strength and durability. He spent hours in this pursuit.

You need to KNOW the child. There is no substitute for close observation in knowing any child. Usually distraction from negative behavior is the best way to redirect his energy.

Let him lead when trying something new. If not interested, don't push it. He will change his mind if he chooses.

Keep the home well below a dull roar at all times. He may learn form the example...again, when and if he chooses.

Cheers!

StanR

What others are saying about identifying the trigger is KEY. Once you are able to think through the things that cause tantrums you have to learn to plan ahead in a few ways:

Transition: use a visual timer so they can see when an activity is going to end and new one will start.
Visual schedules are sooooo helpful when they are nonverbal or having a hard time understanding a change happening.
Light/sound: think about the environment you'll be heading into, I used to bring sunglasses for my son everywhere until he outgrew that particular sensory overload. We also have noise canceling headphones. He hates AC, so we would bring sweaters for him or make sure he isn't sitting under a vent etc
New situations: we have made little "social stories" complete with photos and captions of new places or situations he isn't familiar with. They outline what the event will look like from start to finish. This was GOLD for our airport trip.

These are just some ideas but I can confidently say these things eliminated about 95% of his tantrums. A huge part of it is knowing the source or origin of their tantrum. Good luck!