This topic is discussed in details on the page Tense changes in indirect speech.

When reporting structureThe way in which the parts of a sentence, clause or expression are arranged. E.g.: make somebody + infinitive in "The teacher made me rewrite the composition."s such as wish, would rather, it's (high) time etc., the same rules apply as in the case of reporting second and third conditional sentences.

When reporting a third conditional, we apply no tenseA grammatical category that is marked by verb inflection. To express when an event or action happens in time or when a state exists, we use tenses. changes.

"If they had been more careful, they wouldn't have been killed in the accident", the policeman muttered.
The policeman remarked that they wouldn't have been killed in the accident if they had been more careful.

When reporting a second conditional, the following tenseA grammatical category that is marked by verb inflection. To express when an event or action happens in time or when a state exists, we use tenses. changes may be applied.

When reporting a first conditional, the following tenseA grammatical category that is marked by verb inflection. To express when an event or action happens in time or when a state exists, we use tenses. changes may be applied.

When reporting a zero conditional, the following tenseA grammatical category that is marked by verb inflection. To express when an event or action happens in time or when a state exists, we use tenses. changes may be applied.

No tenseA grammatical category that is marked by verb inflection. To express when an event or action happens in time or when a state exists, we use tenses. changes are made...

(a) if the reporting verbA part of speech that expresses an action or a state. E.g.: John seldom plays tennis. is in present, future or the present perfectThe aspect expressing completion. E.g.: He’s finished university. tenses:

John says he loves you.

(b) if the reported words are always true: