For starters what was removed wasn't the "sound card' it was the sound cards drivers. If the card was remove you would physically need to remove it from the computer and that isn't the case here. Also add/remove programs is under Control Panel; not my computer... is this your first computer?
It's really simple really.
You just need to download the drivers for the card and just run the installer. Chances are you can just find the sound card drivers on the manufactures site. OEM companies like Dell/HP usually have it on their sites too.