Actually, there is an easy way for people to determine which passages in the Bible are poetry.
If you pick up a modern version of the Bible, like the New International Version, poetry will be indented, like so:
Psalm 23
A psalm of David.
1 The LORD is my shepherd, I shall not be in want.
2 He makes me lie down in green pastures,
he leads me beside quiet waters,
3 he restores my soul.
He guides me in paths of righteousness
for his name's sake.
4 Even though I walk
through the valley of the shadow of death,
I will fear no evil,
for you are with me;
your rod and your staff,
they comfort me.
5 You prepare a table before me
in the presence of my enemies.
You anoint my head with oil;
my cup overflows.
6 Surely goodness and love will follow me
all the days of my life,
and I will dwell in the house of the LORD
forever.
Prose passages will not be indented. For example:
1 There was a certain man from Ramathaim, a Zuphite from the hill country of Ephraim, whose name was Elkanah son of Jeroham, the son of Elihu, the son of Tohu, the son of Zuph, an Ephraimite. 2 He had two wives; one was called Hannah and the other Peninnah. Peninnah had children, but Hannah had none.
There is some scholarly disagreement about which Bible passages are poetry and which are not, but not much.