As the commenters have noted, the concept of standing by to fill empty seats for a low fare does not really exist any more, at least on any major carrier. But there do exist situations where you could find yourself landside of security without a boarding pass, yet still needing to get to the gate for onward travel.
For instance, even if your ticket is confirmed, if you do not have a seat assignment and the flight is oversold and checked in full, the airline cannot issue you a boarding pass. For another example, your original flight may be canceled and the airline unable to confirm you on the next flight or two out, but willing to let you stand by for them.
If you find yourself in such a situation domestically, the airline will issue you a Departure Management Card. The actual label may vary— in some cases, it may be indistinguishable from a boarding pass except for being stamped for standby or some such— but in any case it takes the place of the boarding pass and gets you through the security checkpoint. All your other documentation and identification still needs to be in order as usual.
You will be placed on the standby list, from which passengers will receive seats originally assigned to no-shows within the last half-hour or so before the flight. The order on which you are placed on the standby list will vary from airline to airline, each using its arcane balance of frequent flyer status, fare rules, time of check-in, onward connections, and other factors to determine your priority. If they are able to accommodate you, the gate agent will issue you a boarding pass at the gate. If not, you can ask to be placed on the standby list for the next flight.
I have never had to deal with such a situation on an international flight from a country with exit control, and do not know if a DM card would be sufficient to get through it.