Contrary to popular belief, standby is NOT a cheaper fare anymore. Most companies don't even sell standby tickets anymore. The usual way to get them is to either be a dependent or employee of an airline, have a buddy pass, or to already have bought a full priced ticket and just wanting to change the day you fly. The only time you get a bargain is if you volunteered to give up your seat on an overcrowded flight and they upgraded you to first or business class when putting you on standby for the next flight.
For those of you still curious, here is how stand-by works. You should get to the airport at least an hour earlier than normal because they put your name down on a stand-by list which is first come first serve, per say. There IS an order of priority, such as crew members on a schedule first, bumped passengers or passengers who gave up their seats from a different flight second, crew members and dependents not on business next, those with their airline sky mile accounts, unconfirmed open standbys, people with buddy passes, etc.
My advice is:
1.) Make sure that your dates are flexible. You cannot successfully fly standby if you are not.
2.) Call the airline about a week before your leaving, tell them you will be flying standby, how many people are in your party, and ask which dates they think are best. Sometimes they might not do it that way (depending on how their system is set up), so you might just have to ask for how many seat the plane has left for each day of the week you hope to leave. As soon as you find a date that looks promising, put your name on the standby list for that date immediately.
3.0 Call back the night before and the day of your intended departure to make sure that your outlook is still good. No need to go to the airport if there is no chance of getting on.
4.) When traveling standby during the holidays, usually the day of or the day after the actual holiday is easiest to get a seat. I usually have been able to find seats for my family from Europe to the US on 23 December, but before then can be tricky - it can be pretty hit or miss.
While you wait, I suggest you go look around or bring a book to read or something to do. After they do all their upgrades, seat change requests, and board all the passengers with normal fare tickets for that day, they will start to call out the names of stand-by passengers.
Here's the thing to be wary of: if the flight is full, you don't get a seat, so it's always best to call a day ahead and find out how full they expect the flight to be and to give them advance notice that you DO expect to go on the flight for that day.