Если косвенная речь вводиться глаголом в форме настоящего времени, то в придаточном предложении глагол имеет ту же форму, что и в прямой речи.

"I am leaving tomorrow", he says.
He says that he is leaving tomorrow.

"We left home early", they explain.
They explain that they left home early.

"Were you playing the piano all day long?", she asks.
She asks if he was playing the piano all day long.

"Where have you been all this time?", the teacher asks.
The teacher asks where he has been all that time.

Вводное сказуемое (перед that) определяет основную временную плоскость для всего предложения. Если это сказуемое в косвенной речи имеет форму прошедшего времени, то сказуемое в придаточном предложении, при переходе из прямой речи в косвенную, подвергается временному сдвигу.

Present Simple

The girl said: "We are happy here".
The girl said that they were happy there.

"How do you usually get to work?", she asked him.
She asked him how he usually got to work.

Present Continuous

"We are having a really good time at the seaside", she wrote.
She wrote that they were having a really good time at the seaside.

"Are you going somewhere?", the policeman asked the shoplifter.
The policeman asked the shoplifter if he was going somewhere.

Past Simple/Present Perfect

"We went to the cinema last week", they said.
They said that they had gone to the cinema the week before.

"Where have you been all this time?", mother asked.
Mother asked where he had been all that time.

Past Continuous/Present Perfect Continuous

"I was thinking about you all day", the woman said.
The woman said that she had been thinking about him all day.

Past Perfect/Past Perfect Continuous

При переводе из прямой речи в косвенную эти времена сохраняются без изменений.

The businessman said: "I had earned my first million $ by the age of 19".
The businessman said that by the age of 19 he had earned his first million $.

The boy said: "I had been doing my homework for 2 hours when my mother came".
The boy said that he had been doing his homework for 2 hours when his mother came.

Future Simple

"I will come as soon as possible", he promised.
He promised that he would come as soon as possible.

"When will you join us?", she asked.
She asked him when he would join them.

Future Continuous/Future Perfect/Future Perfect Continuous

"We shall be doing a lot of work next Monday", he said.
He said that we should be doing a lot of work the following Monday.

"I will have finished my report by 3 o`clock", he hoped.
He hoped that he would have finished his report by 3 o'clock.

"Next month I will have been working on this play for a year", the playwright said.
The playwright said that the following month he would have been working on that play for a year.

Модальные глаголы, если они имеют форму прошедшего времени, изменяют свои формы при переходе из прямой речи в косвенную.

"I can go there one of these days", he said.
He said that he could go there one of those days.

"It may rain tomorrow", the old man said.
The old man said that it might rain the next day.

"We must go there at once", he said.
He said that we must go there at once.