在【zài】

在 + a place says where someone or something is. On its own it is the whole predicate, so no other verb is needed.

在 + place goes before the verb

When the sentence also has an action, 在 and its place go in front of the verb. English puts the place at the end, and that habit produces the usual mistake.

• × 我吃饭在食堂 → 我在食堂吃饭

A thing needs a localizer, a place name does not

Words like 北京, 学校 and 家 are places already. An ordinary noun is not, so it needs shǎng上, lǐ里, xià下 or another localizer to turn it into one.

• × 书在桌子 → 书在桌子上

Negation

bù zài不在 is the usual negative. méi没zài在 says someone wasn't there at a particular time in the past.

Questions

在哪儿 asks where, and the question word sits where the answer would sit.