Using a comma in a sentence

Should there by a comma in the sentence:

On that day in late September I went to look at puppies.

Should there by a comma in the sentence: "On that day in late September I went to look at puppies."?

Yes, and no, or maybe two, it depends entirely upon the context.

• I'll never forget the day I met Julia. After saving my allowances for months I finally had enough money. On that day, in late September I went to look at puppies.
• I remember when my father finally said we could have a dog. On that day in late September, I went to look at puppies."
• After waiting for months, it finally happened. On that day, in late September, I went to look at puppies.

In each case a different part of the sentence is stressed as important.

In general, think of what the sentence means, of what is most important, then slowly say it out loud. You will naturally pause at certain places and not at others. Those pauses are where the commas belong.