I have a question about using past simple with the future tense. For example, if someone told you something yesterday and what he said will occur tomorrow, which one should you use?
Yesterday , he told me that he would be here tomorrow. or
Yesterday, he told me that he will be here tomorrow.
The first is correct. Would is the past tense of will, and since you are not making a direct quote it must agree with "yesterday".
The person you are talking about is not necessarily still "willing" to be there. Therefore, will takes the past tense, yielding would.
It's unclear from your question what the original utterance was. But I'll assume it was:
"I will be there tomorrow."
Even if this is not the case, you'll learn from this answer how to report whatever the person said. Let's call the person who said the original utterance, Sam, and assume Sam prefers the pronoun he. Meanwhile, I'll use she and her to refer to the speaker, that is, the person reporting what Sam said.
First of all, the speaker can, and will most likely, change the "day words" (and everything else) to match what is true for the speaker. This is why the speaker also changes I to Sam or he and changes there to here: she, the speaker, recasts everything to be according to her point of view. (See Deitic expressions.)
So if the original utterance (said on Thursday the 12th) was 'I will be there tomorrow' and the speaker is reporting this the next day (on Friday the 13th) she would most likely say today.
As for the verb, it depends, again, on the point of view of the speaker. And she has a choice. She can retain will be (most likely by saying 'll be) if the speaker wants to assert that she still believes that the event can happen (In other words, the possibility of the event happening is still true for her). Thus, even if it's 11:59pm Friday and the speaker still has hope/faith that Sam will show up in the next minute, the speaker can, if she wants, say
Yesterday Sam told me that he'll be here today (and I still believe he'll be here even though he only has a minute).
If, on the other hand, the speaker does not see the event as still possible, or she doubts it was ever possible, she can use would (often contracted to 'd):
Yesterday Sam told me that he'd be here today (but I don't think he will or I didn't think he would).
What if Sam has already arrived? In that case, the speaker would usually use would because even though the event came true, it is now in the past.
Yesterday Sam told me that he'd be here today (and he did get here).
To summarize, in reported speech the speaker changes 'deitic words' to match her point of view. This includes the verb: she can, but doesn't have to, retain the original verb tense if she thinks what was originally stated can still occur.
Let's take a quick look at another example:
Sam's original utterance was
I'm going to the movies Friday.
It is now Thursday, the day before the Friday that Sam referred to.
The speaker can say
Sam said he's going to the movies tomorrow.
if she wishes to assert that she believes it true that Sam can make it to the movies on Friday. If the speaker doesn't wish to assert this, or even doubts this, she can say
Sam said he was going to the movies tomorrow.
This leads to an interesting possibility. We use these same "rules" to report our thoughts. Thus, you can get a sentence like
Sam got here tomorrow.
This is short for
I thought Sam got here tomorrow.
The speaker is reporting who she thought would arrive tomorrow. Consider:
A: Sam gets here today, right?
B: Yup. And Tom gets here tomorrow.
C: Wait, I thought Tom got here today. And Sam got here tomorrow.
A & B: You thought wrong.
References: The English Verb, by Palmer (Good Books), and others.
The first one is correct, because if the first side is in past, then the second part is formed by [would + verb] grammatically. You can check this website for clarification: Will or would
