To report something said in the past using a past tense reporting verb, we usually use a tense one step further back in the past. This is called "backshift".

Sue: "I'm getting married". (present) >  She said she was getting married. (past)

Sue: "I met him recently". (past) > She said she had met him recently. (past perfect)

When the sequence of events is clear it is not necessary to backshift past tenses to past perfect.

Sue: "I really enjoyed the party last Sunday". > Sue said she really enjoyed the party last Saturday.

When the reporting verb is in the present, future or present perfect, and the situation is still true, the tenses don't usually change.

Sue: "I love children". > She says she loves children.

Sue: "I'm a vegetarian". > She'll tell you she's a vegetarian.

Sue: "I'm terrified of heights". > She has often said that she's terrified of heights.

When the reporting verbs are in a past tense the modal verbs would, should, could, might, ought to and must do not usually change their form.

Sue: "You should learn to swim". > She recommended that I should learn to swim.

We don't backshift when the reporter sees the past events from the same point of view as the speaker.

Sue: "I was pleased that your exam results were good". > Sue said was pleased that my exam results were good.

We don't backshift with the past perfect.

Sue: "They had already seen it". > She told me they had already seen it".

We can choose to backshift or not when present and future events are still true with past simple reporting verb:

Sue: "Come after lunch" > She suggested (that) I came/come after lunch.

 

Patterns after reporting verbs:

1. verb + that-clause + should

advise, beg, demand, insist, prefer, propose, recommend, request, suggest

They recommended that we should stay overnight in Paris. 

2. verb + to-infinitive

agree, ask, claim, decide, demand, expect, hope, intend, offer, promise, refuse, swear, threaten

Tom asked to write the letter for him.

3. verb + object + to-infinitive

advise, ask, beg, command, encourage, expect, forbid, intend, invite, order, persuade, recommend, remind, tell, urge, warn

I invited them to stay.

4. verb + ing form

admit, deny, mention, propose, recommend, regret, report, suggest.

They regretted having left so soon.

5. verb (+object) + preposition + ing form

accuse sb of, apologise (to sb), apologise for, blame sb for, complain (to sb) about, comment on, confess to, insist on, object to

He accused me of stealing the money.

 

Changes in time and place words 

If the person, place or time of reporting is significantly different from the words in direct speech, we change pronouns and adverbs.

now then, at that time
today that day
tomorrow the following day, the next day, a day later
yesterday the previous day, the day before
next month the following month, the next month, a month later
next year the following year, the next year, a year later
last month the month before, the previous month, the preceding month
last year the year before, the previous year, the preceding year
in two days (weeks) two days from then, two weeks from then
five days ago five days before, five days earlier
five weeks ago five weeks before, five weeks earlier
here there