Direct Speech: He said to me, "I shall help you today."
Indirect Speech: He told me that he would help me that day.
Explanation:
1. The reporting verb "said to" changes to "told" in indirect speech when the subject is a pronoun like "me."
2. The modal verb "shall" changes to "would" in indirect speech when it refers to the future.
3. The pronoun "you" changes to "me" because the speaker is talking to the person being reported.
4. "Today" changes to "that day" to reflect the time shift.
\boxed{\text{He told me that he would help me that day.}}