Several parts combine into one character.

祝 is a compound ideograph: 示 (altar) + 兄 (xiōng, "elder brother" — but originally a pictograph of a person with mouth wide open, performing a religious chant). The unexpected etymological insight: 兄 was originally a religious "officiant" or "chanter" — a person leading prayers — and only later did it shift to mean "elder brother" (the eldest male in a family often led ancestral rites). 祝 thus reads as "the one before the altar, mouth open in prayer, invoking blessing." From this priestly origin grew the modern senses: to bless, congratulate, wish well.

Korean reading "chuk." 祝賀 (chukha, congratulations — universal Korean celebration vocabulary), 祝祭 (chukje, festival), 祝願 (chukwon, "blessing-prayer" = wish / blessing), 祝福 (chukbok, blessing — Christian Korean usage adopted this term for divine blessing), 祝典 (chukjeon, "celebration ceremony" = formal celebration / commemoration). Korean wedding cards open with ("words of congratulations").

Mandarin zhù, 4th tone. 祝 (zhù, to wish / pray for), 祝贺 (zhùhè, to congratulate), 祝福 (zhùfú, to bless), 祝愿 (zhùyuàn, to wish — formal). The conversational phrase 祝你好运 (zhù nǐ hǎoyùn, "I wish you good luck") and 祝你生日快乐 (zhù nǐ shēngrì kuàilè, "I wish you a happy birthday") are essential Mandarin pleasantries; 祝~ followed by a noun is a productive blessing pattern.

Japanese on-reading シュク (shuku) — 祝賀 (shukuga, congratulations), 祝日 (shukujitsu, "celebration day" = national public holiday), 祝祭日 (shukusaijitsu, "celebration-festival day" = holiday). Kun-reading いわう (iwau, "to celebrate") — 祝う (iwau), お祝い (oiwai, "celebration / felicitation" — used for birthdays, weddings, promotions, and other life milestones). Japanese culture of お祝い involves elaborate gift-giving and ritualized congratulations: お祝いの言葉 (oiwai no kotoba, congratulatory words), お祝い金 (oiwaikin, gift money in special envelopes for weddings and other auspicious occasions).

Memory aid: an altar (示) plus a mouth-open priest (兄, originally an officiant) — the prayer leader before the altar = blessing.