How do you teach egg moves to pokemon?

You can teach Egg Moves to a Pokémon via breeding. You will need a female Pokémon and then you will need a compatible male Pokémon with the respective Egg Move and then you can put the 2 into the Daycare and the Pokémon Egg will result into an offspring of the female Parent with the male's move.

An example is using a female Bulbasaur. You can use a male Roselia that knows Grasswhistle, putting the 2 of them into the Daycare together will create a Bulbasaur Pokémon Egg that will result in a Bulbasaur that knows Grasswhistle which is 1 of Bulbasaur's Egg Moves.

Another example is using a female Charizard. You can use a male Axew that knows Dragon Pulse and putting them together in the Daycare will result in a Pokémon Egg that will hatch into a Charmander that knows Dragon Pulse.