My daughter was 2 1/2 when my son was born. The entire pregnancy we talked about how her baby brother was growing in my belly just like she did. When he was born, we showed her my scar (had a c-section) and explained to her that they took her baby brother from mommies tummy. When we came home, each day, no matter what, I set time aside just for her - even if it was just 10 minutes to read a book, she got alone time with mommy. We also constantly remind her how she used to be this little and got even more attention than her brother cause we didn't have to share our attention with anyone else. I also encourage her to help with him. Whether it's bringing me a diaper or playing with him with one of his toys when he is fussy and I am busy cooking or such, she loves to help. He is now 5 months old and she will be 3 in a month and they are amazing together. She talks and sings to him all the time. She loves to play patty cake with him and insists that we read his book (Goodnight Moon) together each night before bed. I honestly think our constant dialog with her and having her help with the baby helped her adjust well to him being part of the family.
Now she does still have the occasional toddler meltdown, but its not due to her brother. We have been going through a struggle of her not listening to Mommy, but doing everything Daddy says. After not picking up her toys as requested for the 100th time, I finally took ALL her toys away. She would ask for them and I explained to her that she doesn't get her toys until she listens to Mommy when I ask her to do something. She went three days without her toys, but when I asked her to pick up her toys last night before bed, you can bet she picked every single toy up (I do help of course, but she was capable of making the mess, she knows how to pick it up as well).
It may take something drastic like that for it to sink in that she needs to behave. I found that if the tantrum gets so bad, it can't be controlled, the best thing to do is put them in a safe spot (crib, bed, strapped in her carseat if your out) and ignore the tantrum. She will eventually calm down and realize that she gets ignored when she throws a tantrum.