Debbie Drown, Educator, Principal, says:

Tantrums in two year olds are not unusual, although can be difficult to handle. It is important for you to remain calm so that she doesn't get a reinforcing reaction from you. The first thing you may want to do is try to figure out if the tantrums are occurring in response to certain situations. The next time your daughter throws a tantrum, try to remember what happened just before the tantrum and respond accordingly. For example, if the tantrum occurs because she is afraid of something, be careful to avoid a similar situation. However, if the tantrum occurs because she can't have something she wants in the grocery store, tell her that she won't get to go with you again until the tantrums stop and then follow through. The important thing is not to give in to the tantrum just to make it stop. As hard as it is for you, if the tantrum occurs in a public place, remove her from that situation until the tantrum stops. Then explain that the behavior was inappropriate. If the tantrum occurs at home, try to ignore the behavior unless she is becoming dangerous to herself. The tantrums should lesson if they do not get the expected response.