"Does Scripture tell us how to be discerning?"
It certainly does.
Discernment is the process of making careful distinctions in our thinking about truth. The discerning person is the one who draws a clear contrast between truth and error. No one can be truly discerning without developing skill in separating divine truth from error.
Paul sums up the process in 1 Thessalonians 5:21–22:
“Examine everything carefully; hold fast to that which is good; abstain from every form of evil.”
There, in three straightforward commands, he spells out the requirements of a discerning mind.