A move tutor (Japanese: わざおしえ人 Move Teacher) is a non-player character who will teach a Pokémon moves that are not normally able to be learned through level up, TMs, or HMs. Move tutors are found in Kanto, Johto, Hoenn, Orre, and Sinnoh. They are not to be confused with move relearners.
Johto move tutors
Crystal
In Pokémon Crystal, an elderly fellow visits Goldenrod City's Game Corner every Wednesday and Saturday after the player has become League Champion. He teaches three different moves for 4000 coins, two of which were TMs in Generation I and returned to that status in Generation III, and one of which later became a TM with the other two. These moves are breedable in the same fashion as TMs and HMs.
HeartGold/SoulSilver
The following tutorable moves are available in Johto's remakes, Pokémon HeartGold and SoulSilver. Similar to Emerald most of the moves that a move tutor can teach to a Pokémon require a set amount of Battle Points. Fourteen of these moves are exclusive to HeartGold and SoulSilver, while the rest are obtainable in Platinum.
The following moves are also available in Pokémon Platinum, but with the difference that most require BP instead of shards as payment:
The following moves are only available to the move tutor in Pokémon HeartGold and SoulSilver:
Kanto/Sevii move tutors
These move tutors are in FireRed and LeafGreen. They do not appear in the older versions for the Game Boy system.
Normal move tutors
These tutors will teach a Pokémon a move otherwise unobtainable with the current, Generation III TM list. Many of the NPCs which gave a TM containing a move in Generation I that is no longer available in TM form in the current generation will directly teach the move they would have given instead. These can only be taught once.
Special move tutors
A woman at Boon Island's Cape Brink will teach one move to each of the fully evolved Kanto starter Pokémon. She will teach Frenzy Plant to Venusaur, Hydro Cannon to Blastoise, and Blast Burn to Charizard. The moves can only be taught to Venusaur, Blastoise or Charizard and the Pokémon learning the move must have maximum happiness.
Hoenn move tutors
In Pokémon Emerald, various move tutors can be found across the Hoenn region. Some moves may be purchased at the Battle Frontier. Those that cannot be purchased may only be learned once from the tutor.
Orre move tutor
In Pokémon XD: Gale of Darkness, there is a move tutor in Agate Village.
Mew, when transferred over from any game to Pokémon XD, can learn other moves with the purchase of 5,000 Poké Coupons. Though this can only be done after beating the game, it can be done multiple times. Mew does not normally learn the following moves, but is able to do so through the use of this move tutor.
Sinnoh move tutors
Diamond/Pearl
There are two Move Tutors in Sinnoh - one on Route 228 and one on Route 210. The move tutor on Route 210 teaches Draco Meteor to a Dragon-type Pokémon which has had its happiness maximized. Similar to the Cape Brink move tutor in FireRed and LeafGreen, the Route 228 Move Tutor will teach one of the elemental versions of Hyper Beam to a fully-evolved starter with maximum happiness. Unlike the Cape Brink tutor, it can be any of the twelve starter Pokémon, but the move's type will always correspond with the Pokémon's primary type. Also unlike the Cape Brink tutor, it can be taught as many times as the player likes.
Platinum
In Pokémon Platinum, in addition to the move tutors in Diamond and Pearl, three new move tutors are added, in Snowpoint City, on Route 212, and in the Survival Area. These move tutors accept shards in return for their services, charging eight shards of various colors per move.
Red Shards emphasize power.
Blue Shards are for special effects.
Yellow shards are for status problems.
Red Shards are what I like!