Having a Pokemon with the Ability Flame Body or Magma Armour in your party will roughly halve the amount of steps it takes for an egg to hatch. You don't need to use any moves, as long as it is in your party it will take effect.
For example, let's say we are trying to hatch a Froakie egg. A Froakie egg takes approximately 5355 steps to hatch. Let's say we have a Talonflame in the party, and it has the Ability Flame Body. The amount of steps it takes for the Froakie egg to hatch now will be roughly 2677 steps, due to Talonflame's Flame Body.