You cannot find a Moon Shard in Pokémon HeartGold. The Moon Shard was an item that was created exclusively for Pokémon XD since there wasn't time in XD so the shard was the only way to evolve Eevee into Umbreon.
You can get some in the underground tunnels with your explorer kit you can get in other then that try going to Pastoria City and enter the Pastoria Great Marsh contest. Pokeballs are laying all around Pastoria Great Marsh with different color shards in them.
Added by "Xantrac":
If you have a Star Piece, you can go to the Fuego Ironworks near Floaroma Town, and talk to Mr Fuego. He will give you one of each color Shard in exchange for a Star Piece
there are these shacks in which there are move masters. each master wants a different color shard. they will teach your Pokemon a move for a certain amount of shards of the color they want.
At the end of Victory Road, there are 3 breakbale rocks. The Second one contains a blue shard.
Theres 1 in Violet City beside the pokecenter in heartgold and soulsilver
You can get shards in various locations but the best way to get shards is off Pokémon underwater.
u go underground and dig into a wall
you find them in rocks using rock smash
underground u idiot
There are four shards in Pokemon Platinum which are the red, blue, green and yellow shards. These can all be found in the Underground and they are also held by certain Pokemon. I know that Corsola can hold a red shard and that Relicanth can hold a green shard. The shards can be traded with various move tutors who will teach your Pokemon an attack in exchange for a certain combination of shards. The three move tutors are found on Route 212, in Snowpoint City and in the Survival Area.
shards can be used to trade with other people. in return, they may teach your Pokemon moves. there are 3 move tutors in Pokemon platinum that will teach your Pokemon moves in exchange for shards in a specific color.
You can either dig them up in the Undergound or you can find them on the ground all over Sinnoh by using the Dowsing App. on the Poketch.
Violet City - the juggler next to the Poke Center
there is this guy in the sea at sunyshore city then you talk to him and he changes all the shards into stones or you can buy the NDS action replay ultimate code for Pokemon and get 999x stones of every kind
There are four shards in Pokemon Platinum- red, blue, green and yellow. They can all be found in the Underground.
The color shards you can find in Pokemon Platinum are Red, Blue, Green, and Yellow Shards.
You need 6 Red Shards and 2 Green Shards in order for the Move Tutor in Pokémon Platinum to teach Ancientpower to 1 of your Pokémon.
There are four shards in Pokemon Platinum which are the red, blue, green and yellow shards. These can all be found in the Underground and they are also held by certain Pokemon. I know that Corsola can hold a red shard and that Relicanth can hold a green shard. The shards can be traded with various move tutors who will teach your Pokemon an attack in exchange for a certain combination of shards. The three move tutors are found on Route 212, in Snowpoint City and in the Survival Area.
You cannot find it as a hm in platinum but some Pokemon can learn it naturally. You can get from the move tutor on route 212 for 2 red shards, 4 blue shards and 2 yellow shards. HOPE THIS HELPS
There is a move tutor west of pastoria city who will teach it to one of your Pokemon for 6 blue shards and 2 red shards ;)
You can get them underground.
Mining and digging Underground.
shards can be used to trade with other people. in return, they may teach your Pokemon moves. there are 3 move tutors in Pokemon platinum that will teach your Pokemon moves in exchange for shards in a specific color.
if a Pokemon holds a plate (arceus) and a Pokemon uses flail the shards restore the plate because flail breaks the plate.
If you mean Pokemon Ruby, Sapphire or Emeraldm, they can be traded with a hunter on an island halfway between Lilycove City and Mossdeep City. Pokemon Platinum shards are used to tutor moves to Pokemon on Route 212, Snowpoint City, and the Survival Area.
They can't be bought. You can find them underwater, or attached to wild pokemon. Chinchou have yellow shards, Clamperl have blue shards, Relicanth have green shards and Corsola have red shards.