You can get this quest in a few ways. The most likely way is for you to find or receive a special holotape from a doctor in the wasteland. You can also get it by going into Dr. Li's lab and talking to Dr. Zimmer.
The first goal is to figure out who exactly it is. Zimmer will want you to seek out some of the Replicated Man Holotapes if you haven't already. You can start with Dr. Preston, but just about every doctor in the wasteland will have one. They are also not preset, so when you find one it will always be the next in the series.
You need to find the 4th in a "tier" system to get a concrete idea of where to go. The sympathizers on the railroad, the slavers, and mechanics will also have some. The easiest course is going to the doctors though. You can look for more, but it's a little pointless.
You can also just cheat and listen to me. It doesn't matter whether you find him through an investigation or if you stumble into it.
Also, once the quest starts, you should be contacted by a woman named Victoria Watts. She'll give you an Android Component and ask you to tell Zimmer that he died. This is an absolutely awful course. Do not do this! You'll only get 50 caps and the location of the Temple of the Union as a reward.