Hi, and welcome to Using English.
You do if what follows is a direct quote.
He was screaming that we should follow him.
He was screaming, "Follow me!"
This is from the Purdue Online Writing Lab:
Mr. Johnson, who was working in his field that morning, said, "The alien spaceship appeared right before my own two eyes."
Martin Luther King Jr. said of the Emancipation Proclamation, "This momentous decree came as a great beacon light of hope to millions of Negro slaves who had been seared in the flames of withering injustice."
Who said, "Fame means when your computer modem is broken, the repair guy comes out to your house a little faster"?
Your question was concerned with a direct quote. In the US, at least, the standard is that a comma is required.
Omitting the comma is actually incorrect in the US. Now I know that including it is incorrect in the UK.
I would not say that including a comma is incorrect in BrEng on the basis of one respected BrEng style guide. I simply quoted from this to illustrate that usage is a matter of opinion.
In academic writing, a comma is prescribed:What do the Aussies do, Ray?