Reported Speech

We use reported speech to give information about what people say or think.
Saying exactly what someone has said is called direct speech, what a person says appears within quotation marks. For example: She said, "I am going to the cinema tomorrow."

Indirect speech (or reported speech), doesn't use quotation marks and the tense usually changes. This is because when we use reported speech, we are usually talking about a time in the past and the verbs, therefore, have to be in the past too.
For example:

Direct speech	Indirect speech
"I'm going to the cinema", he said.	He said he was going to the cinema.

Direct speech		Indirect speech
Present simpleShe said, "It's cold."	›	Past simple  She said it was cold.
Present continuous  She said, "I'm teaching English online."	›	Past continuous  She said she was teaching English online.
Present perfect simple  She said, "I've been on the web since 1999."	›	Past perfect simple  She said she had been on the web since 1999.
Present perfect continuous  She said, "I've been teaching English for seven years."	›	Past perfect continuous  She said she had been teaching English for seven years.
Past simple  She said, "I taught online yesterday."	›	Past perfect  She said she had taught online yesterday.
Past continuous  She said, "I was teaching earlier."	›	Past perfect continuous  She said she had been teaching earlier.
Past perfect  She said, "The lesson had already started when he arrived."	›	Past perfect  NO CHANGE - She said the lesson had already started when he arrived.
Past perfect continuous She said, "I'd already been teaching for five minutes."	›	Past perfect continuous  NO CHANGE - She said she'd already been teaching for five minutes.

Modal verb forms also sometimes change

Direct speech		Indirect speech
will  She said, "I'll teach English online tomorrow."	›	would  She said she would teach English online tomorrow.
can  She said, "I can teach English online."	›	could  She said she could teach English online.
must  She said, "I must have a computer to teach English online."	›	had to  She said she had to have a computer to teach English online.
shall  She said, "What shall we learn today?"	›	should  She asked what we should learn today.
may  She said, "May I open a new browser?"	›	might  She asked if she might open a new browser.

Note - There is no change to; could, would, should, might and ought to.

Time change: If the reported sentence contains an expression of time, you must change it to fit in with the time of reporting, we need to change words like here and yesterday if they have different meanings at the time and place of reporting. In addition if you report something that someone said in a different place to where you heard it you must change the place (here) to the place (there).

Expressions of time if reported on a different day
this (evening)	›	that (evening)
today	›	yesterday ...
these (days)	›	those (days)
now	›	then
(a week) ago	›	(a week) before
last weekend	›	the weekend before last / the previous weekend
here	›	there
next (week)	›	the following (week)
tomorrow	›	the next/following day

Pronoun change: In reported speech, the pronoun often changes.
For example: "I teach English online", she said. becomes She said she taught English online.

Reporting Verbs

Said, told and asked are the most common verbs used in indirect speech.

We use asked to report questions. For example: I asked Lynne what time the lesson started.

We use told with an object. For example: Lynne told me she felt tired. (Note: Here me is the object)

We usually use said without an object.For example: Lynne said she was going to teach online.

If said is used with an object we must include to. For example: Lynne said to me that she'd never been to China.

Note : We usually use told. For example: Lynne told me (that) she'd never been to China.

There are many other verbs we can use apart from said, told and asked.

These include: 

accused, admitted, advised, alleged, agreed, apologised, begged, boasted, complained, denied, explained, implied, invited, offered, ordered, promised, replied, suggested and thought.

Using them properly can make what you say much more interesting and informative.

For example:  He asked me to come to the party: 

He invited me to the party.

He begged me to come to the party.

He ordered me to come to the party.

He advised me to come to the party.

He suggested I should come to the party.

Use of 'That' in reported speech

In reported speech, the word that is often used. However, that is optional.
For example: He told me that he lived in Greenwich. / He told me he lived in Greenwich. Note - That is never used in questions, instead we often use if.For example: He asked me if I would come to the party.

Exercises to practice:
http://www.ejerciciodeingles.com/ejercicios-discurso-indirecto-rellenar-huecos/

Source: https://www.learnenglish.de/grammar/reportedspeech.html