[verb / adjective] + 者
[verb phrase] + 者
[number] + 者
者 goes after a verb, an adjective or a whole verb phrase and turns it into the person – or occasionally the thing – it describes. It does the job of 的人 in writing, and it attaches directly, with no 的.
Rules use 者 to name who a provision covers: 迟到者, 未经许可者, 获奖者. The phrase before 者 can be long, which is where it saves most space over 的人.
Many everyday nouns are 者 words that have set: 作者, 读者, 记者, 学者, 消费者, 志愿者, 爱好者. New ones are still formed the same way – 参与者, 成功者, 失败者.
After a number, 者 counts things already mentioned: 二者 or 两者 "the two", the first step toward 前者 and 后者.
Classical Chinese marks the topic of a definition with 者 and closes it with 也: "X 者,Y 也" means "X is Y". It survives in quotations.
者 replaces 的人 rather than adding to it, and it doesn't attach to an ordinary noun.