A Moon Ball has a 4x catch rate on Pokémon that evolve with a Moon Stone or belong to evolutionary families of the former. It can be obtained by crafting it, buying from a shopkeeper, or as a tier 1 special drop,
The Moon Ball has an increased catch rate on:
To craft a Moon Ball lid, one cooked Blue Apricorn, one cooked Yellow Apricorn and one cooked Black Apricorn are needed. Placing the 3 cooked Apricorns in a row horizontally in a crafting table, in that order, will produce two Moon Ball discs, and then using them with an anvil and a hammer will make them into Moon Ball lids.