How do you know the oxidizing agent of a reaction?

The oxidizing agent is the substance being reduced, where it gains electrons and causes the oxidation of the other substance. Oxygen is typically an oxidizing agent.

Oxygen the element from which the name Oxidizing agent came from has the second highest electronegativity of all the elements.
The high electronegativity means that Oxygen will have an greater pull for the electron density in a bond with other elements, giving Oxygen a net negative charge and the other element ( except Fluorine) with a net positive charge.

Elemental Oxygen # O_2# has a charge of 0 as the electron density is shared equally between the two equal Oxygen atoms.

When Oxygen combines with Hydrogen the electron density is not shared equally. Hydrogen has an electronegativity of 2.2 less than Oxygen. So in the reaction between Hydrogen and Oxygen, Oxygen will gain electron density and Hydrogen will lose electron density

# 2 H_2 + 1 O_2 === 2 H_2O#

In # H_2O# Oxygen has a charge of -2 and Hydrogen has a charge of +1
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Oxygen has gone from 0 to -2. Oxygen has been reduced and is the Oxidizing agent.

Hydrogen has gone form 0 to +1. Hydrogen has been oxidized and is the Reducing agent.

The element that has an increase in negative charge is the oxidizing agent, and this is the element with greatest electronegativity.