Now at first I was hoping that by "in-game virtual pet" the writers meant a sort of Tamagotchi that virtual players themselves carry for entertainment. That would be a fun image -- some Paladin obsessing over a pixilated space baby as it slowly succumbs to an AIDS-like pandemic.
But instead they mean a "real" pet in the virtual world. Geez, confusing the orders of simulacra is so nineteen-eighties!
Here's exactly how to transfer the disease, assuming you are a high-enough level character to not die from it immediately:
1. expose your pet to the disease
2. dismiss your pet (this stops the countdown timer on the disease)
3. go to an area with same-faction players
4. recall the pet (this starts the disease counter again)
5. pet infects people
Players have not missed the AIDS parallel as this screen shot shows. This thread contains a player discussion.
This is similar to the situation that occurred in May 2000 in the Sim virtuality, where a dirty guinea pig lead to death and transmitted infections.
Remember kids: always clean your virtual pets.
Tamagotchi is a tiny pet from cyberspace who needs your love to survive and grow. If you take good care of your Tamagotchi pet, it will slowly grow bigger, healthier, and more beautiful every day. Bit if you neglect your little cyber creature, your Tamagotchi may grow up to be mean or ugly. How old will your Tamagotchi be when it returns to its home planet? What kind of virtual caretaker will you be?
No, hold on, I'm a real caretaker surely?