The shards can be found by looking around the underground.To look in the underground you need the explorer kit. You get that early in the game. If you are far into the game and still don't have it go to some of the earlier towns like Hearthome, and Sandgem, or Eterna, and Oreburgh, and Jubilife, and Floaroma and talk to every one there.
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yellow shard and red shard and green shard
Red Shard Blue Shard Yellow Shard Green Shard Violet City and Fuchsia City
The moon shard was in a Pokemon movie, and it was apparently given out as a Promo item, along with the sun shard.
Blue Shard- Route 124; Wild Pokemon. Green Shard- Route 126; Wild Relicanth. Red Shard- Route 124; Wild Pokemon. Yellow Shard- Route 126; Wild Pokemon.
I think it just combines by themselves. What happened to me was that I had the Courage shard and the Power shard and I byed the Wisdom shard. When I got all three of them in my inventory it was combined.