What is the correct way do an apology or offer an apology?

The Word apology is a noun, a Word for a regretful acknowledgment of an offense or failure; a formal expression of one's regret at being unable to attend a meeting or social function; a very poor or inadequate example of; a reasoned argument or writing in justification of something; a Word for a thing.

A noun functions as the subject of a sentence or a clause, and as the object of a verb or a preposition.

Example sentences:

An apology will help make her feel better. (subject of the sentence)

They sent an apology for being unable to attend. (direct object)