During a trip I had recently my plane was delayed for a couple of hours before leaving Montreal so I got to Chicago late and missed my connection. I was a bit concerned because I had an important meeting the next day in Southern California.
The first thing I did was call the United airlines toll free reservations number and the people there told me that I had already been put on a flight the next day. This was not going to help me because I had a meeting the next day. They recommended that I talk to customer service.
It took more than an hour of waiting in line because United only had three customer service agents on duty, and when I got to the front of the line there were a couple of hundred people behind me. The customer service person we met did not seem interested in helping too much. They did not offer anything at all. This surprised me because I have been stranded at other airports and been offered hotel rooms for the night. No, all I got was them telling me that the earliest they could get me to San Diego was by the next evening. I asked her to get me to Los Angeles or Orange County and she told me that I would still only get to SanDiego by next evening. I had to explain that if she could get me to Los Angeles or Orange County I would drive the rest of the way. Then she finally understood.
So, I was put on a flight to Orange County and drove a couple of hours to my hotel. The only problem I had is that my bags were sent to San Diego- so I had to pick them up the next day.
Funnily enough I was in a hotel room a couple of days later watching a report about how only 75% of all flights are on time. This does not seem reasonable to me. You can see the statistics for yourself at the Bureau of Transportation. Scroll down the page and click on Airline On-Time Performance.
If you have the unfortunate but common experience of missing a connection the first thing you should do is call the airline. I recommend doing this while waiting in line at customer service. If you do need to be somewhere: try to fly to another airport else which is relatively close to where you are going- and drive the rest of the way.