Hair transplants - how do they work?

I don't think that I'm the typical hair transplant candidate, mainly because I'm female, but also because I'm pretty young (29) which makes it suck that much more. Following a particularly stressful event three years ago, I began to lose my hair. It was diagnosed as telogen effluvium and I was told that my hair could possibly grow back but it hasn't. I'm left with some pretty severe bald patches on my scalp and above my temples. It's not enough hair loss to wear a wig and I'd REALLY rather not wear a wig. I feel like a hair transplant could be the answer for me since I have a base of hair to work with. My problem is that I don't really understand how a hair transplant works, what the process is, et cetera, and I guess I'm afraid that I won't be eligible. Any and all input will be welcomed.