Several parts combine into one character.

Pictograph: a person (大) astride / climbing onto a tree (木). The encoded scene: someone mounting / boarding. The character covers boarding vehicles, mounting horses, and abstractly "taking advantage of" or "multiplying" (in math). Three forms: 繁體 乘 / 新字体 乗 / 简体 乘 — Japan simplified by removing the bottom strokes, Mainland China kept the traditional form (one of the rare cases where simplified Chinese is more complex than Japanese shinjitai).

Mandarin: chéng, rising 2nd tone. 乘车 (chéngchē, board a vehicle), 乘客 (chéngkè, passenger), 乘机 (chéngjī, board a plane / take an opportunity), 乘法 (chéngfǎ, multiplication — math), 乘以 (chéngyǐ, multiplied by). The mathematics meaning is essential — 三乘以四 = "3 times 4". Note that for "ride" in everyday speech, 坐 (zuò, sit) is more common: 坐车 / 坐飞机 (board car / plane).

Japanese: on-reading ジョウ (jō) for compounds — 乗車 (jōsha, boarding a vehicle), 乗客 (jōkyaku, passenger), 乗用車 (jōyōsha, passenger car), 搭乗 (tōjō, boarding — used at airports for boarding announcements). Kun-reading の.る (no.ru, to ride / get on) is a high-frequency verb — 電車に乗る (densha ni noru, take the train) is foundational. Transitive partner の.せる (no.seru, to give a ride / load on): 友達を車に乗せる (give a friend a ride).

Note the meaning split: 乗る pairs with the particle に (location-marker) — 電車に乗る, not 電車を乗る. Mandarin's 坐 likewise pairs with vehicles directly: 坐火车 = "take the train".

Memory aid: a person mounted on top of a tree — climbing/boarding.