Catch a Jigglypuff and a Ditto or catch both male and female Jigglypuff and bring them to the fourth island in the Sevii archipelago. You'll find a day-care center there. Of course, you'll need to complete the Elite four challenge before getting there.
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It is Igglybuff.
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.
In the trophy garden its a daily Pokemon :D
In Pokemon firered you can't, but in Pokemon leafgreen you can get it then trade it to Pokemon firered.
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.