Momofmany is correct.
Step over your daughter while she is throwing a fit. Do not say a word. Try not to even look at her.
If she follows you, tell her "Mommy needs a time out." Go to your own room or go to the bathroom and shut the door.
To ward off the tantrums, try offering options instead of a no.
She says "I want a cookie".
You can say, "how about some peach slices or apple slices?"
She does not want to put on her shoes. "Ok, I will give you 2 minutes and THEN you can put on your shoes."
Also remember children like to know what to expect. Give her a heads up about what the plan is. "Today we will be going to the grocery store. You can play for 10 more minutes and then you need to put all of your toys into the toy box." "I like how you put away your toys. "
"Remember we do not buy snacks at the store. Pick out a snack and put it in my purse."
Remember at the store we use inside voices in the store."
If she is having a tough day, it may not be a good day to go to the store, or you may need to wait till she has had some running around outside.. Or maybe see how she is after nap.
Ask her to "use her words."
Ask her if "she needs a hug."
Try to see what brings on the melt downs. She is at the age when she wants to do everything herself. So give her the time to do this or.. let her know.. "today I am in a hurry, so lets see how fast mommy can put your shoes on your feet. On your mark, get set, here we go.. .."