There's 7 right now in the game. The first, you get by completing the minigame on the Desktop menu. The other 6, by beating nights with certain plushes you find in the shop, those being the Nile Plush and Sammy Plush. When you see them in the shop, buy them, put one of them on your desk and beat the night. One video = one night beaten. There's 2 for Nile and 4 for Sammy by the way.
Also, you may notice the Poppi Plush (i think that was the name, i don't remember) in the shop and think it unlocks that animatronic's videos, but sadly there aren't any in the game yet.