Study materials
One sentence can be reported neutrally, or a single word can carry the whole intention of the speaker.
"I didn't do it." → He said he hadn't done it.
"I didn't do it." → He denied doing it.
Precise reporting verbs save words and add judgement. There is one price: each of them has a grammatical frame of its own.
Why not just say
Say and tell report the words but stay silent about the intention. A precise verb packs into one word what would otherwise take a whole sentence.
He said that he had taken the money.
He admitted taking the money.
The only trouble is that each such verb pulls its own grammatical frame along. It is learned together with the word, exactly as in the topic on gerunds and infinitives.
Frame one: that
The simplest pattern. The verb, then a whole clause, and the word that may be kept or dropped.
She explained that the office was closed.
He admitted that he had made a mistake.
Say, explain, admit, deny, claim, insist, complain, announce and many others work this way. It is the safest option when a verb's pattern slips your mind.
Frame two: the infinitive
Verbs of promising, agreeing, refusing and offering take to plus the action. No addressee is named.
She promised to call me.
He refused to sign the contract.
They agreed to postpone the launch.
Promise, agree, refuse, offer, threaten and decide belong here.
Frame three: the ing form
Verbs of admitting, denying and proposing an action take an ing with no preposition at all.
He denied taking the money.
She suggested moving the meeting.
Admit, deny, suggest, recommend, mention and regret work this way.
The mistakes everyone makes
The first is taking an infinitive after a verb that wants an ing.
He denied to take the money. → He denied taking the money.
The second is taking an ing after a verb that wants to.
She promised calling me. → She promised to call me.
The third is adding an addressee where none belongs.
He suggested me to move the meeting. → He suggested moving the meeting.
All three are caught by one question. What frame does this particular verb take? If you cannot recall, use that: it fits almost always.
Try it right now
Recall three remarks from yesterday's conversations and report them in English with precise verbs: one with that, one with an infinitive, one with an ing.
Then check whether you managed to avoid say and tell entirely.