In modern language, drama queens are people who often make small incidents or situations into bigger issues than they need to be. They may become emotional to the point of being theatrical over things that others don't respond to in this manner. The best way to talk to such a person is usually to first tell her to calm down and then let her know that you won't discuss anything until she does speak and behave calmly.
Calming anyone who is over-excited or speaking loudly may help her stop and think before acting out. Of course, people who are known as drama queens are typically used to behaving in a loud or disruptive manner anytime something isn't to their liking. Try to figure out if the person is seeking attention or genuinely upset. If it's the latter, try gently explaining the reasons why there is no need to be upset to try to calm her fears. If she seems to be making a fuss mainly to be the center of attention, you should mention that you feel embarrassed by her over the top behavior and you won't be a part of any future similar situations.
You could try to remind the person that others are affected by her behavior and deserve a calmer approach. Drama queens are often thought of as being selfish and may be sensitive to being called on that; rather than calling them names, just point out the situation as you see it. Gently say that there is no need to blow things out of proportion because it makes things worse for everyone else. Make useful suggestions for solving the problem to avoid the conversation becoming about blaming the person for overreacting.
By focusing on developing a solution together, rather than arguing, further fuss can usually be avoided. Some overly dramatic individuals may not necessarily want to create attention to themselves by speaking loudly or behaving inappropriately. They may be simply be used to immediately reacting to their emotions, rather than thinking things though first. Be kind and help the person to think before acting. It isn't easy to talk about this to someone as she is likely to feel insulted, which may easily lead to more bad behavior; speaking about it in a light, humorous, non-judgemental way during a dramatic episode is often best.
