I've done this a couple of ways. The first is to run a one shot featuring a current PC at a prior point in time while the other players run NPCs. The purpose is to spotlight something or someone in the character's past. This works alot better than the player simply saying, "Oh, that's my arch nemesis so and so", but if there is too much detail already in the back ground can become quite forced and flop.
The second is more of the flashback or tale as told by a stranger. Here I can adapt to whatever the players do. With this I'm usually trying to convey more information and its not unusual for the story to take several sessions. One can even jump back and forth between the two story lines which is great if your players like cliffhangers.