Flying space available is great. It is cheap, fun, and can be very flexible. However, when things get busy you can find yourself in trouble. Space available travel is prioritized and if you aren't an employee of an airline, you'll find yourself at the bottom of the pile.
You can mitigate your troubles by always arriving for the earliest flight possible. Quite often people oversleep and miss the early flights. Waking up at 3:30 AM to possibly catch the 5:00 AM flight might sound awful, but it may be the only way to make it to your destination.
If you are not able to make it onto a flight you are listed for, you are automatically rolled over to the next flight. However, twice I have not been rolled over for one reason or another and had to be manually moved. Always double check to make sure you have been added to the next flight.
When you miss a flight, it may seem tempting to use the 1-800 number most airlines have to change to a different option. However, I've found they tend to not get the change made properly. Always use the gate agents to make the change and quite often they will also suggest alternate routes (if only to get you off their back).
If you happen to be woefully unlucky and are bumped from one day to the next save your boarding pass from the day before. You can use that to skip the lines at the ticketing counter and go straight through security. Once you get to the gate double check that you are indeed listed on the flight and get yourself a new flight coupon (or if really lucky a boarding pass).
The last bit of advice is to be as sociable as possible. Hang out with the gate agents, any flight attendants who are stuck, and yuck it up with other space available passengers. I've met so many great people sitting around in airports waiting on flights. Some of these people can even help you out if you're really stuck, so it's worth being polite and friendly. Getting somebody a $3 airport coffee can go a long way towards making it onto a flight.