As others have pointed out the A class is a first class seat, in exchange for a full-fare coach ticket. The ticket is actually confirmed first class, not standby. Naturally, there are a limited number, so advance purchase helps.
You can shop around to find the flight and carrier with this fare available. Generally not available on wide-body planes. UA, US, NW, and DL have this fare in many markets. Perhaps others do as well.
It is my understanding that D ticket is a business class upgrade for full fare coach, but I have not seen any available. Perhaps those who have can share their experience with me, since I have been looking for a discounted business class fare.
John