Verizon FiOS → Thinking of getting fios internet

does verizon install fios internet in the apartment, or does the customer do a self install

That depends if the apartment previously had FIOS.
If the ONT is there, you can do a self-install.
If there is no ONT, then a tech visit is required.

At least here in Westchester County, NY, if the building is wired for FIOS, they just run the cable to all the apts.; they don't install ONTs until you actually order the service, and then a tech comes to install the ONT (in our building in the kitchen), run the cable to TVs and router (which of course can be in another room), etc. As More Fiber says, if there's already an ONT you may be able to do a self-install (if you want to), but at least here, when someone moves out, VZ takes the ONT back.