Learned Moves
As your Entei gains experience and levels up, it will learn moves naturally. It starts with Bite and Leer at level one. It learns Ember at level 11 and it learns the rest of its moves every ten levels up through level 81. These moves are Roar, Fire Spin, Stomp, Flamethrower, Swagger, Fire Blast and Calm Mind. Ember, Fire Spin, Flamethrower and Fire Blast are fire-type moves that do various levels of damage. Bite and Stomp are normal moves dealing damage. Leer, Roar, Swagger and Calm Mind do not do damage but rather affect the statistics of your Entei and its rivals.
TM Moves
Technical Machines, or TMs, are items that allow you to teach a move to your Pokemon. These moves are not permanent and can be overwritten by learning other moves in the future. Some of the TMs you can teach to your Entei are moves it will learn on its own, but you can use the TM to teach it the move at an earlier level. The TMs your Entei can learn are Calm Mind, Roar, Toxic, Hidden Power, Sunny Day, Hyper Beam, Protect, Rain Dance, Frustration, Solarbeam, Iron Tail, Return, Dig, Double Team, Reflect, Flamethrower, Sandstorm, Fire Blast, Facade, Secret Power and Rest. These moves are a mixture of fire, poison, psychic, rock, grass, steel, water and normal types. Some deal damage while others affect battle in other ways.
HM Moves
Hidden Machines, or HMs, are similar to TMs except the move learned is permanent and a single HM can be used repeatedly while TMs can only be used once. HMs are also moves that can be used outside of battle to affect the environment. The HMs Entei can learn are Cut, Strength, Flash and Rock Smash. Cut slices down trees that block your path. Strength allows you to move rocks. Flash lights up darkened areas such as caves. Rock Smash allows you to destroy large boulders that block your path.
Tutor Moves
Tutors are scattered throughout "Pokemon." They exist to teach your Pokémon special moves that you can't get from a TM, HM or from learning naturally. The moves that your Entei can learn from tutors are Body Slam, Double-Edge, Endure, Mimic, Mud-Slap, Psych Up, Sleep Talk, Snore, Substitute, Swagger and Swift. Body Slam, Double-Edge, Mud-Slap, Snore and Swift are attack moves. The rest affect battle in various non-attack ways. Mimic is notable as it allows your Entei to copy the enemy's most recent move and use it against them.