You have to breed a (female) Jigglypuff or Wigglytuff.
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In Pokemon Crystal, Igglybuff evolves into Jigglypuff when it reaches level 2. Igglybuff is a baby Pokemon that evolves relatively early compared to other Pokemon. Evolution levels are consistent across different generations of Pokemon games, so this information applies to other games in the series as well.
Pichu, Cleffa, Igglybuff, Togepi, Tyrogue, Smoochum, Elekid and Magby.
You can only get it from breeding it from Jigglypuff or Wigglytuff
Each day, if you talk to Mr. Backlot in the mansion south of Hearthome, he'll say there is a certain Pokemon there. For the next two days, that Pokemon will appear randomly in the trophy garden. Igglybuff is one such Pokemon.
Apparently you can't find Igglybuff in the wild; you have to breed Jigglypuff or Wigglytuff with Ditto, or, you can breed a female Jigglypuff or a female Wigglytuff with male Pokemon from the Fairy Egg Group.