You can either earn it by beating the Elder at the top of the Sprout Tower after seeing your rival, or by purchasing it on the 5th floor of the Goldenrod City Department Store.
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Mimic is not a TM. In HG/SS, there is also no Move Tutor that teaches Mimic.
You can obtain the TM Sunny Day from the Radio Tower located in Goldenrod City.
Professor Oak's assitant will give it to you. Oak's assistant WON'T give it to you. He does that in RBY/FR/LG. In Pokemon Gold, Silver, Crystal, HeartGold and SoulSilver, the Elder in Sprout Tower will give it to you. In GSC, Flash is a HM, in HG/SS it is a TM.
Use PokeSav in D/P/Pt, or use an all-tm/hm learnable code for HG/SS.
You get it in Sprout tower. You can also buy it in the Goldenrod department store. In HG/SS games it is TM70.