How can you tell? In what qualitative way is a believer who supposedly has the Holy Spirit different from a typical non-believer?
The bible tells us so. In Acts, after Pentecost, we see that everyone who received salvation also experienced the subsequent baptism or infilling of the Holy Spirit with power.
Acts 8:17
Then Peter and John laid their hands upon these believers, and they received the Holy Spirit.
Acts 8:19
“Let me have this power, too,” he exclaimed, “so that when I lay my hands on people, they will receive the Holy Spirit!”
Acts 10:47
“Can anyone object to their being baptized, now that they have received the Holy Spirit just as we did?”
Acts 19:2-7
“Did you receive the Holy Spirit when you believed?” he asked them.
“No,” they replied, “we haven’t even heard that there is a Holy Spirit.”
3 “Then what baptism did you experience?” he asked.
And they replied, “The baptism of John.”
4 Paul said, “John’s baptism called for repentance from sin. But John himself told the people to believe in the one who would come later, meaning Jesus.”
5 As soon as they heard this, they were baptized in the name of the Lord Jesus. 6 Then when Paul laid his hands on them, the Holy Spirit came on them, and they spoke in other tongues and prophesied. 7 There were about twelve men in all.