Wait 73 hours then go to where you recruited them,they should be there...if not check the hall of the dead in the hold you recruited them from...
its possible they might have died you will have to give more info who was your follower where the went missing and all that if you can not see them go to hall of dead of city where your follower lives and you might find their dead body their
In the Dark Brotherhood Sanctuary...where you recruited them...once you wait 3 days or more.In addition,the Initiates are marked Essential,and will not die.
Are you playing on PC or game console?
If PC, save your game in a new slot and then type the following in the console: player.moveto 00015D09 to teleport to this follower's location in the game. Make note of the location, then reload the save you just made and fast travel to her location.
If you play on PS3, you will have to load a saved game prior to losing her (assuming you have one).
If you don't, you likely won't be able to use another NPC follower due to how the developers made the follower system work in the game. You can only have one follower at a time, unfortunately and when one bugs up you're in trouble without a previous save. In your case, the female Dark Brotherhood Initiate is set as "essential" in the game, meaning she can't die, so if she is stuck somewhere, you may come across her again. Try "retracing your steps" by thinking about where you last saw her and maybe you can still salvage your game.
I know it's hard not to be upset, this happened to me once and I decided to start a new game because of it, but it helped me to learn to keep plenty of backup saves. By, the way, if you have a USB or other external storage device that you can plug into your PS3, you can always transfer a few older saves onto it, in case you run into trouble again. I am not familiar with the specifics of the PS3, but I'm pretty sure it works similarly to the Xbox 360 with transferring (or moving) saved games to an external device.