Speaking from experience I would say that 90% of tantrums in our house result from communication misunderstandings. Either I don't have the time to stop, listen and explain (usually mid household chore!) or that we have misunderstood each other.
I've seen so many posts about 'big feelings' recently. Both adults and children alike experience these but as an adult we can process them at least. When a tantrum is starting to boil there are lots of signs and diffusing it early really can save you and your child a lot of stress.
Talking about feelings. I try to talk about how my kids are feeling throughout the day or when something is happening. For example, my eldest (4 years) is about to start school so I've found that asking her over the past few weeks how she is feeling about it has helped to get her to think about how she feels and to process those feelings. Even my youngest (2 years) has been coming out with 'Kit angry!' when something doesn't go his way or 'Kit sad' if he is crying.
Modelling behaviour is another way- your child will be copying what you do the majority of the time, so if you scream and shout when you are angry then the chances are that so will they. By simply explaining to them that you are angry and that you are going to take a deep breath and calm down shows them that you are calmly dealing with your anger without shouting. One of my favourite ways to get my eldest to calm down is to get her to sit calmly, imagine there are 10 candles in front of her and to slowly blow them all out.
Feeling overwhelmed is something we all feel at times and being given the chance to process it is so important. We have a 'Calm Down/Thinking' step (the step above the naughty step!) which is used when the littles need to take a moment to have some quiet time if they are erupting, often they will take themselves to it if they feel the need. We never use it as a punishment- they are allowed to take a toy on it, it isn't timed and they can talk to us if they like.