才 (cái) and 就 (jiù) both go before the verb and show how the speaker feels about the timing. 就 says something happened early, quickly or easily; 才 says it happened late, slowly or with difficulty.
Time + 就 + verb + 了. Time + 才 + verb.
Both words come after the time word and straight before the verb. 就 says something happened earlier than expected. 才 says it happened later than expected, like "not until" in English. For something that has already happened, a 就 sentence usually ends in 了, but a 才 sentence doesn't.
The same idea works with lengths of time and with ages. With 就, it took less time than expected or happened at a young age. With 才, it took a long time or came late.
Straight before a number, 才 means "only": the speaker thinks the number is small. It is often used with ages, clock times and prices.
After a condition, 就 means "then": if the first thing happens, the second follows. 才 means "only then": the second thing happens only if the first one does.
The most common mistake is putting 了 at the end of a 才 sentence about the past. Say 他十点才来, not 他十点才来了.
Neither word can go at the end of the sentence. When they mean "late" or "early", put them after the subject and the time word, straight before the verb.
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