However, it's rather difficult to construct many kinds of questions without ending in a preposition, as evidenced by these examples.
How does this fit in?
What page does this go on?
Where do we go out?
Many a grammar snob (which I guess I am) turns up his or her nose at these constructions, but then turns right around and uses them. Yet these constructions are actually correct. They are not always the best, but they are correct, with one stipulation: they are not appropriate for formal (typically academic) writing.
The Scribner Handbook for Writers notes that prepositions, as their name indicates, are meant to be placed before their objects, "the noun or pronoun it connects with another part of the sentence." They usually initiate a prepositional phrase, which (you may remember from a few weeks ago) must be followed by a comma.
So don't you worry too much about using those prepositions at the end of a phrase. They are okay! Of course, you should watch for unnecessary prepositions, like the one in my title. "Where's my preposition?" covers all the meaning necessary. "At" is not needed, because I've already asked where the preposition is. The Scribner Handbook for Writers offers another example of unneccessary prepositions:
"We met up with the director at noon."
This sentence could simply be said like this:
"We met the director at noon."
If you're trying to reach a word requirement for a paper, you could leave in the "up with," but if you're trying to be clear and concise, you don't need them. Now, I'm generally predisposed to over-wordiness, so I'm not one to talk about being concise, but in my experience, teachers and professors seem to like it. I'd recommend the shorter sentence in formal writing, but otherwise, I think you could let it go.
Today's Source: DiYanni, Robert, and Pat C. Hoy II. The Scribner Handbook for Writers. Pearson Longman: New York. Fourth Edition. 2004.