You cannot reason with a 2-year-old, especially one in the throes of a tantrum! The key is to "extinguish" the behavior by ignoring it, which is easy enough to do at home (leave the room), but many tantrums happen while at stores. In those cases, there are 2 things you can do--ignore the child (in the cart-seat) while at the grocery store check-out (where she's screaming for candy!) or pick her up and carry her out of the store/mall while she kicks and screams and get her into her carseat, then you can sit in the driver's seat and take slow, calming breaths.
This behavior cannot be given in to or tolerated, otherwise the tantrums will get worse (since she has gotten what she wanted from throwing them in the past...). Depending on how strong-willed your child is, it could take years to get beyond this (sorry), but you have to win every time (and not let anger overtake you). You are establishing yourself as the authority figure, which will serve you well as she gets older and as she moves into teenhood!
If possible, leave her with a sitter or join a baby-sitting co-op, and when you go shopping or out for lunch etc., you can let her know that she will not be going with you because her behavior is unaccaptable. Then you can try her out over time, taking her along, but first telling her what is expected of her behavior-wise. You can start a behavior-modification thing where she gets to choose one thing at the grocery store and if she doesn't cooperate, she loses even that one thing. (My third would then demand TWO or nothing! So--she got NOTHING!)
My first child (now 25) threw tantrums at stores when she wanted something, so I would tuck her under my arm and take her, kicking and screaming, out of the store. My second daughter (21) was compliant. My third (18) threw multiple tantrums every day for years--exhausting! EVERYthing was a control issue for her. Often the at-home tantrums would last for over an hour (she would get herself all worked up), so I learned to go into her room after a short while and hold onto her strongly while rocking her, and she would eventually calm down. She is still strong-willed and very intense but learned to control her temper/feelings over time.
I am still alive, and so are they--and the teen years have been mostly wonderful, because they grew up with boundaries and (somewhat grudgingly) allowed me to be the mom! At least with teens you can reason and let them know that rules have much to do with your love and worry. 2-year-olds couldn't care less about YOUR feelings--they are the center of their world.
:o)