To recognize a preposition, find it together with the noun phrase that follows it, then ask what relation that unit expresses: in under the table, under points to a position relative to the table. A preposition links a noun or pronoun to other words in the sentence; the details of how it does this are covered in the definition article.
Place: the keys are under the table (position).
Time: since Monday (starting point).
Direction: walked towards the door (movement path).
Abstract: a cup of tea (possession or tie).
Recognition guide by function
Place: the letter is between the books. Ask where something sits in space; in, on, between all answer that question.
Time: since Monday. Ask when or for how long; at, in, for, and since pin a moment or a stretch to the calendar.
Direction: she stepped into the room. Ask about a path of movement; to, into, from trace where something goes or comes from.
Abstract relation: a gift for her sister. No space or time involved; for, of, by, with carry ties like possession, instrument, or cause.
Manner and purpose: with great passion, left for the meeting. Ask how something is done or what it is for.
Phrase role, not a fifth function: whole phrases like after dinner or with great passion work as optional adverb-like detail. The preposition itself still expresses place, time, manner, or purpose, so classify the relation first. When the whole phrase seems to fit another label, remember that two descriptions can both be true at once, and the section below explains how to sort out that overlap.
When two labels fit the same phrase
The trickiest boundary is between the preposition's own meaning and the job its whole phrase does. The book on the shelf is both a place phrase and an adjective-like detail describing book. Classify the relation the preposition expresses first, place here, then note the phrase's role separately if needed.
Test it: ask what the preposition plus noun answers about the head it modifies. Arrived before noon answers when, so it works like an adverb. A man in a hat answers which one, so it works like an adjective. The preposition in stays spatial in both cases.
Most prepositional phrases act as adjectives or adverbs, and only rarely as nouns, though this frequency is a general impression rather than a measured rule. So on Monday is time in meaning even though the phrase behaves adverbially; the two labels describe different layers and can both be true.