The tenses generally move backwards in this way(Backshift of tenses)

from to
Simple Present Simple Past
Simple Past Past Perfect
Present Perfect
Past Perfect
will would
Progressive forms
am/are/is was/were
was/were had been
has been
had been

Tense Direct Speech Reported Speech
present simple “I like ice cream” She said (that) she liked ice cream.
present continuous “I am living in London” She said she was living in London.
past simple “I bought a car” She said she had bought a car OR She said she bought a car.
past continuous “I was walking along the street” She said she had been walking along the street.
present perfect “I haven’t seen Julie” She said she hadn’t seen Julie.
past perfect* “I had taken English lessons before” She said she had taken English lessons before.
will “I’ll see you later” She said she would see me later.
would* “I would help, but..” She said she would help but...
can “I can speak perfect English” She said she could speak perfect English.
could* “I could swim when I was four” She said she could swim when she was four.
shall “I shall come later” She said she would come later.
should* “I should call my mother” She said she should call her mother
might* "I might be late" She said she might be late
must "I must study at the weekend" She said she must study at the weekend OR She said she had to study at the weekend

* doesn’t change

Occasionally, we don’t need to change the present tense into the past if the information in direct speech is still true (but this is only for things which are general facts, and even then usually we like to change the tense):