Move the verb back a step when the thing said has stopped being true, or when you have no idea whether it still is. Leave it exactly where it stands when it plainly still is, because she said she was a doctor and she said she is a doctor are two different reports, and only one of them leaves her a doctor.
The shift is not an obligation that comes with the word said. It is a small piece of distancing, the same movement that puts a verb one step back to mark something as unreal, and a listener reads it that way whether or not you meant anything by it.
Eight sentences that show the shift
- the tense shifts back one step. Present becomes past, past becomes past perfect, and will becomes would. It is mechanical and it is the whole rule.
- He said he was tired, reporting I am tired. The present has moved back and the pronoun has changed with the point of view.
- She told me she had finished, reporting I have finished, so the perfect moves to the past perfect.
- say, tell and ask. Tell needs a person after it and say does not: he told me but he said to me. This is the commonest error in the topic.
- He asked if I was coming. A yes or no question becomes an if clause and loses question word order entirely.
- She asked where I lived, not where did I live. The reported question takes statement order, which is the second commonest error.
- He told me to wait. Commands become an infinitive, with no tense shift at all, which is the easiest of these to produce.
- tomorrow becomes the next day. Time and place words shift with the tense: here becomes there, this becomes that, now becomes then.
Two steps back, and then the language runs out
A present form goes back one step and a past form goes back one more, and there the movement stops. Is late becomes was late. Arrived becomes had arrived. Had arrived stays where it is, because English has no third step to offer, which is why a long report of a long conversation flattens out: everything that happened before it ends up wearing the same form.
Some words never move, and they are not exceptions to anything. Will call becomes would call because would is the stepped form of will. Would, could and might are already stepped, so might come is reported as might come and there is nothing to learn beyond noticing which forms are back a step to begin with.
Where it stops: the shift becomes a reflex
Every exercise on this subject requires the shift, because an exercise that sometimes required it and sometimes did not could not be marked. Several hundred of them installs a reflex, and the reflex outlives the exercises. A learner then reports something currently true in the stepped form, and it comes out as doubt they did not intend: he said he was from Brazil, about a man standing in the room, sounds like a report of a claim rather than a report of a fact.
The stall holds because English speakers rarely correct it. Both versions are grammatical, so there is nothing to repair, and the listener simply comes away slightly less sure about Brazil. Nobody involved knows anything went wrong.
The same reflex hides the half of this that is genuinely hard, which is questions. A reported question loses its inversion and its question mark: he asked where I was going, never he asked where was I going. That one is not invisible. Every native speaker hears it, and it survives to a high level in learners who can shift a tense perfectly.
Reading the same sentence reported four ways
Google News is free and it does one thing here that no exercise can. Put a quoted sentence from a public statement into it, open four write-ups of the same statement, and look at what each reporter did with the tense. Some shift and some do not, and the ones that do not are usually signalling that the claim still stands. Google News replaced buying four papers on the same morning, which is what this comparison used to cost.
Read the body text and not the headlines. Headline English drops auxiliaries and marks tense by its own conventions, so a headline tells you nothing about what the reporter decided, and it is the paragraph underneath that carries the decision.
What it looks like when it goes wrong
Three failures, in order of how long they survive. The reflex shift on something still true, which almost nobody catches. The uninverted question, which everybody catches. And the one in between: shifting the verb and forgetting everything else that pointed at the moment of speaking, so I will see you here tomorrow is reported a week later as he said he would see me here tomorrow, where here and tomorrow are still anchored to a room and a day that have both gone.
The forms being moved are the ones described in which form of the verb, and what each one says about time, the distancing itself is the same movement as in if, would, and the four ways English talks about what might happen, and the formal way of reporting a claim without naming who made it is when what was done matters more than who did it. All three sit under the rules that decide what a sentence is allowed to mean.
The question underneath all of this is not about tense at all. Reporting somebody means choosing a verb for the reporting, and said, claimed, admitted and insisted carry far more attitude than any backshift does, which makes it a choice about the words rather than the grammar: emails, essays and reports that read like a native wrote them.