were can I find the person to teach my Pokémon Zen Headbutt in Pokémon y

There is no straight-up move tutor in this game. The closest you'll get is the move reminder in Dendemille Town.

There's two guys that teach moves, but one only teaches ultimate moves to the different starters and the other teaches a move to some dragons or something.

Closest thing is probably the move Reminder guy as Itwongo mentioned. You can trade a heart scale to learn a forgotten move, and like in other games you can also learn some of their ultimate moves that way as well. Good way to get heart scales is to Wonder trade a bunch of times and use pokemiles to buy some, or catch a bunch of luvdisc and 50% of the time theyll have a heart scale. You can also just use thief on them.

There's actually several move tutors through the game, but none of them are the same as most move tutors in previous games. One of them will teach any starter pokemon (from any gen) their "ultimate" move. Another will teach any starter Grass Pledge, Water Pledge, or Fire Pledge, moves that are especially effective when used in double and triple battles. one other one will teach a Dragon pokemon Draco Meteor. Some moves that used to be tutor moves could possibly be given to a pokemon as an Egg move now, since TM moves can be passed down.

To get an Egg move onto a pokemon, find a male pokemon that can breed with the pokemon species you want in the end that knows the move you want (the move MUST be compatible with both species. Not all pokemon can learn all moves etc etc) The pokemon you want the move on should be female in this case as well (if you don't have a female, breed it with ditto until you do.) Then let the two get frisky in the daycare until you have an egg. Hatch it and the offspring has a possibility of knowing the move.

Oh and one more thing. If both parents know a move, that will be passed down as well. This is often the method used for getting a Legendary Catcher Gallade. Get a gardevoir with hypnosis (female) and a Ghastly, Haunter, or Gengar that knows Hypnosis and Mean Look (male) and breed them until you get a male Ralts with Mean Look and Hypnosis. Level that up to 20 to get Kirlia, then give it a Dawn Stone. Continue leveling up the resultant Gallade until it learns False Swipe by level up (or use the TM for it) and now you have a pokemon that can prevent its victims from running away, make them fall asleep, then leave them with 1 HP, making them as easy to catch as they ever will be.

One thing that caught my attention in this game is that they explicitly tell you that TMs can be used as many times as you want. Has that always been the case and I just never realized it?