In English, at least according to Chomskyan generative linguistics, a particle is a word that supplements a verb without having any meaning of its own. Consider the following examples:

The noders threw around the idea of meeting in Bhutan.
Japan Airlines flight attendants strap down their passengers with clever knots.
John Romero stood up Bill Gates at their date.

The words around, down, and up, while looking like prepositions, actually do nothing but change the meaning of the verbs preceding them. Nothing is actually going around, down, or up.

So let's take two sentences, one using a particle and one using a preposition:

John Romero stood up Bill Gates.
John Romero stood up the street.

How can you tell whether a particle or preposition is being used? There are three tests to find out. The first is called "cleft construction," where you reverse the order of the sentence so that the object comes before the subject and verb. If the sentence still works, you're dealing with a preposition. Consider the following:

It was up Bill Gates that John Romero stood. (no way! but I bet he'd love to try)
It was up the street that John Romero stood. (way!)

The second way is called "conjunction." Assuming that you're dealing with a preposition, simply tack on another prepositional phrase. If the sentence still works, you're dealing with a preposition.

John Romero stood up Bill Gates and over the hill. (huh?!)
John Romero stood up the street and under the overpass. (perfect!)

The final way is called "particle movement." Assuming that you're dealing with a particle, move it to the end of the sentence. If the sentence still works, you're dealing with a particle.

John Romero stood Bill Gates up. (yes!)
John Romero stood the street up. (nope! unless there was an earthquake, and he was really strong.)

So what's the functional difference between a particle and a preposition? Simply put, a particle changes the meaning of the whole verb. A preposition only tells you how the verb, in its basic form, is being carried out. If you "throw up thirty gallons of Mr. Pibb on the tea cups" ("up" being a particle), you're not actually throwing anything, and a non-native speaker of English might become very confused. On the other hand, if you "throw up confetti on New Year's" ("up" being a preposition), you are literally throwing something.

Linguistics is awesome!