First of all I really need to stress, she is not being naughty, she merely has no other way of expressing her needs, wants and frustrations.
Then, I have found that there are various things that trigger tantrums in both my boys, Brandon is pretty much over his tantrum stage, but he (actually both boys) used to throw whoppers of note when he was tired, hungry or wanted my attention, so I tried to avoid these situations - made sure he was rested and had eaten on "schedule". A
But there are times when it is simply impossible to give your full, undivided attention eg when you are rushing to get ready in the morning,driving, cooking etc, so try to involve him a bit.
In the morning let him help by choosing his cereal, what he wants on his toast or passing you your mascara / creams.
Talking does help, but the secret is repetition, repetition and more repetition ! You will need to say the same thing so many time times it will drive you crazy and still they will "forget" and do it anyway until one day the idea will stick and then you move onto the next thing.
Time out is good when they have reached the point of no return, when the temper has turned into a full blown tantrum - all this really does is let him know that you cannot / will not put up with uncontrollable screaming.
That said I need to add : Time out worked a dream with Brandon. With Liam, removing me from his immediate enviroment was like a brutal beating to him, so I would sit on the floor and let him try get on my lap, but I would not make any contact with him, it all came from him - all the time I would say "I do not cuddle screaming boys, once you have calmed down I will cuddle you" It was terrible for the first few times, but each time his crying became less, and he can pretty much calm himself down without me now.
I also found I had too many rules, so all I was doing was saying no, someone said that I should choose about 5 rules to enforce eg, brushing teeth, sit in your car chair, we all sit at the table until everyone has finished eating, don't pour out my shampoo / shower gel, keep your fingers out the plugs, and work on those until they have got it, then add another.
And most of all - don't even start a battle if it is not VITAL that you win, if you give in cos you realise it's not really that important, you are giving the message that the harder he screams the more likely you will give in.