It is a kind of a fear that we all have. It actually has happen to me many times that a flight gets cancelled and on a few occasions I have even missed my flight. Once it was because of a lot of traffic, another time because of a miscalculation of the distance of the airport and another because my flight was actually on the day before and I got confused about the date. Anyways missing a flight for any reason creates a lot of stress and frustration, despite that one needs to stay calm and analyze the options to make the best decision.
I have experienced how difficult it is more and more now to deal with schedule changes and cancellations. It used to be more or less that if a flight was cancelled for any reason most passengers were rebooked and hotel and food was provided. Now these kinds of resources are limited or even nonexistent. At the same time we see fewer disruptions. In fact it is not a good business for airlines to deal with these kind of situations, so they try to keep their airplanes flying.
In case that a flight is delayed the first thing to do is to stay calm and find some answers. The question to ask is what the cause of the delay or cancelation is. If it is because of weather, airlines are normally less willing to provide for food or hotels or any other kind of compensation. They normally will help to reschedule with no cost. In these situations that are beyond the control of anyone it is important to be friendly, acknowledge the frustration of everybody and ask for help in a nice way. Try to be the first arriving to the counter, or even try to call the airline or the travel agency who booked your flight since they may be able to help. Remember since resources are limited these are normally given in a first come first serve basis.
If the cause of delay is the fault of the company, the passenger may be entitled to compensation. Ask about such a thing with a firm but respectful voice. Take advantage of your status, if you are a frequent flyer say so, but do not lie about it, since it is enough to take a quick look in the computer to know the truth. A lot of time passengers get more if they volunteer themselves to take a different flight.
If it happens that one misses a flight because of bad traffic, or just a misunderstanding with time, there is when one needs to be even more friendly with the personnel. The general rule is that if one misses a flight it is one’s fault and a new ticket should be bought. In my case when this has happened and it was not in a low cost airline friendly words have helped me a lot. Being nice has gotten me into another flight without paying penalties, but no one can be assured of this.
The general rule is: stay calm, analyze your possibilities, be firm but friendly and be flexible so you may end up arriving at your destination on time and even with some extra dollars in the way of a voucher.