I see lots of posts about trying to save a trip when the flights go wrong. There are a bunch of things you can do to help keep things on track and get a better result when it all goes bad.

1. Try and book the entire flight sequence on one PNR or tyflight record. This insures someone owns your problem.
2. Try and minimize non mainline flts. The airlines try and present a seamless product but the reality is they subcontract almost all the lift under 90 seats. Those sub contracted flights can be hard to spot when booking but they have to tell you. They have a much lower on time and completion factor. If you can't avoid them leave yourself connection buffers if able. This problem is getting worse as the connection carriers are facing a severe pilot shortage.
3. If you are checking bags get them to the counter 1 hour prior to the flight. In plain view inside the bag place a paper with contact info for where you will be on vacation not your home. TSA must check and release all bags before the airline can load them. If you check them 35 minutes prior to the flight they might not make it.
4. Have a fully charged cellphone with your airlines reservation number loaded. The minute you know your flt schedule is disrupted or canceled call reservations and start working on a alternative. Don't go stand in line behind the other 100 passengers trying to get rebooked at the airport. There are limited seats and you are competing for them. The quicker you get rebooked the better.
5. Understand your options when rebooking and keep in mind you don't have to accept a auto rebook if it's not the best solution. Keep in mind that with most airlines you can demand to be moved to another airline if it's a better option. Going to the islands Spirit will not rebook at all. Jetblue and SWA normally will not rebook but if you can make a compelling case they might. They may have to cut you a check in that case and send you to the ticket counter for the new airline since they don't participate in the rebooking system.
6. Be at the gate 30 minutes prior and make sure you have the right time zone. They will cancel seats 15 minutes prior to issue to standbys if you have not boarded. Watching the last 5 minutes of the game is not worth missing the flight.
7. When dealing with reservations be polite but if your not making progress ask for a supervisor. They have more authority to fix things. If your inconvenienced ask for miles in compensation. They often are easier to get then other options. Keep in mind that each res agent can and will add notes to your passenger record. If you are rude or use foul language the next person you speak with will know that.
Part two to follow.