Adding information to a photo is a whole lot easier than removing it. Think of it this way: You can teach a photo manipulation program how to draw hair, and you can have it find the edges of a person’s face and put hair there because it’s just drawing on top of what’s already there. But how do you feed it someone with hair and ask it to show you what’s underneath it? It can be done in a generic sort of way, but you’re unlikely to find it in consumer software. The best you’ll be able to do in most consumer products is cloning and healing.
Cloning is taking portions of an image from one place and painting them into another. Just about any half decent art program will have a clone feature.
Healing is more or less the same thing, but it also maintains the hue and tone map of the area you’re painting over, thus making it look more natural. I don’t know anything other than Photoshop that has a heal feature.
It would be difficult to explain the exact process of cloning and healing to “remove” (really, paint over) the hair on someone’s face, but I can say it is a painfully slow and tedious manual process with very little automation involved. I don’t know of any other way to do it.
The stuff you see on CSI or Law & Order? Pure Hollywood.