Privacy Invasions are marked on your map as diamond-ish ovals, that have a hole in them (to some they might look like an eye).
Sometimes, you will be able to intrude after you gain access by "hacking" in the digital world to unlock, and at other times, you will need to unlock lines in the "real world" by opening the profiler and following the white lines to each unlock source (some are unreachable and need you to use a camera to unlock certain boxes).
You can finish these without completing the story, as they are always available, but you will need to ctOS tower in Pawnee to be able to see them on the map for that area.
Also, you can just hack into the main camera, and once you see a picture, in the top right corner it will show you that you have finished that Invasion with a progress counter. You do not actually have to hack the phones / tablets / cameras inside once you have access, nor do you have to listen to the full dialogue (though the dialogues / actions are fun to watch, like the girl talking about her boyfriend as he is outside her door, lol).
Included below is a guide for all 30 peephole missions, done by AFGuidesHD.