How did AIDS spread, exactly?

I don't understand how it could affect so many people if it was spread by er, merely fucking, given that it originated in Africa recently.

I had a friend who got HIV from working with a woman who was in the early stages of AIDS.  They barely even knew each other.  Doctor said it was probably because of a tiny bit of blood that no one noticed, possibly even transmitted on a piece of paper.  Fuck that.  I refuse to work or even be near anyone with HIV.  Period.  Luckily my friend moved upstate so I didn't have to deal with shutting her out, but I've already quit a job because I found out there was someone there with HIV.