有 is a hand (the ナ/又 on top) holding a piece of meat (月 here is 肉, "flesh", not moon). To hold meat in your hand is to have it — the abstract idea of possession grew straight out of a fist closed around food. The single most important thing to learn here: the 月-shaped element is flesh, not the moon.

Mandarin: yǒu, 3rd tone, and the 8th most frequent character in the entire language — it appears in almost every sentence. 有 (yǒu, to have) pairs with its negation 没有 (méiyǒu, to not have); 我有 (wǒ yǒu, "I have") is the basic frame of possession. 有名 (yǒumíng, famous, "have a name"), 所有 (suǒyǒu, all / ownership).

Japanese: on-readings ユウ (yū) and ウ (u); kun-reading あ.る (aru, to exist). 有名 (yūmei, famous), 所有 (shoyū, possession), and most beautifully 有り難い (arigatai) — literally "difficult to exist", i.e. rare and precious. The everyday Japanese "thank you", ありがとう (arigatō), descends directly from this 有.

Korean hanja-sound "yu": 有名 (yumyeong, famous), 所有 (soyu, ownership), 有無 (yumu, presence-or-absence). It draws the most basic line there is — between what exists and what does not.

Memory aid: a hand (ナ) over meat (月) — what the hand grips is what you "have".