How do you pronounce the H in "an historian"?

A lot of people I know argue that you should use the article "an" before words such as "historian", "history", "hotel", "hospital", "heretic". I don't want to debate whether or not this is correct or merely pretentious affectation, but I'm curious about how it should be pronounced.

If I decide to use "an" before "historian", should I pronounce the H? Should I say "an historian" or "an istorian"?

[Edited:] My advice would be not to pronounce the h after an. This what I have always heard style books recommend.

I assumed that most people, if not all, who use an did not pronounce the h. I certainly can't remember ever hearing h pronounced after an; but it is always very dangerous to predict whether something is always or never the case. Wait, let me rephrase that: it is nearly always very dangerous... The main cause of this danger is that there will nearly always (see, I am learning) be exceptions. Even so, I believe they are exceptions; if someone disagrees and provides a decent argument or evidence, I will edit this answer again.

The use of a versus an in English is almost entirely based on whether the next word is pronounced as a vowel or not. The way it is spelled usually does not matter; compare a user, an honour. Based on this pattern, the advice of style books, and what I suspect is the pronunciation of a large majority, pronouncing the h with an seems like a bad idea. The fact that some people on this very page and elsewhere perceive it as "affected", and that it will displease traditionalists, would seem reason enough to drop either the h or an. A traditionalist might think, "hey, that guy is trying to sound cool, but he fails miserably, because he doesn't quite understand how it works", even if the speaker did in fact understand, but simply made a different choice. Such is snobbery.

The NOAD I had on my Mac Mini had a note similar to the following one, which Oxford Living Dictionaries reports about an and its usage with words starting with h.

Is it "a historical document" or "an historical document"? "A hotel" or "an hotel"?
There is still some divergence of opinion over which form of the indefinite article should be used before words that begin with h and have an unstressed first syllable. In the 18th and 19th centuries, people often did not pronounce the initial h for these words, and so an was commonly used. Today the h is pronounced, and so it is logical to use a rather than an. However, the indefinite article an is still encountered before the h in both British and American English, particularly with historical: in the Oxford English Corpus around a quarter of examples of historical are preceded with an rather than a.

The pronunciation reported by the Oxford Living Dictionaries for hotel is /hoʊˈtɛl/, and for historical is /hɪˈstɔrək(ə)l/; similarly, the pronunciation of historian is /hɪˈstɔriən/.

Usually not.

For the most part, as Cerberus says, the use of a vs. an is based on whether the next word is pronounced with an initial consonant or not; so an would only be used when the h is pronounced.

However, the peculiar case of an historic etc. is one of those times when prescriptivism/snobbery/etc. has affected the language too much to be separable from “natural usage”. I know many people whose accent would normally pronounce the h of historic, but who subscribe on more or less deliberately affected grounds to an historic, in writing and (less often) in speech. From memory, I’m fairly sure I have heard it spoken sometimes as an historic with the h pronounced.

However, I can’t find to find audio/video evidence online to back this up. The two examples of an historic I’ve found so far: A US congressman (at about 06:46:50), who gives it no h that I can hear; and a New Zealand librarian (at 00:24), who has no distinct h but has, I think, perceptibly more aspiration than after an than there would normally be for a following vowel.

There appear to be people who say "an historian", pronouncing both the "n" and the "h", in the U.K. I don't think this is the case with most American speakers who use "an" with "historian". Let me explain what I think is going on.

In my speech (a variety of American English), an /h/ in an unaccented syllable following a consonant is either not pronounced or absorbed into the consonant, so the consonant becomes slightly more aspirated. See this question. So in "their historical building" the /r/ and the /h/ merge together to form a slightly breathier /r/. And after most consonants, the /h/ vanishes entirely. This wouldn't happen with "their histories", where the /h/ is in an accented syllable and thus pronounced.

You can see that both "an istorian" and "a historian" are consistent with this system for pronouncing /h/. Which one a speaker says is probably a matter of what they heard when they were learning English. Most speakers of American English use "a" with "historian", but there is a minority that uses "an". Speakers who use "an" would say /hɪˈstɔriən/ after a vowel, but say /ənɪˈstɔriən/, either without the /h/ or with a very faint /h/. The same speakers would also drop the /h/ in the sentence "I find historians interesting."

As some evidence that this is really what is going on, I recently heard within the space of two or three minutes the same speaker of American English say "a historical" /əhɪˈstɔrɪkl/ with the "h" and "an istorical" /ənɪˈstɔrikl/ without it.

This question is a little bit like asking "what is the correct pronunciation of 'an biscuit'?". You're asking for the 'correct' pronunciation of a form which is essentially ungrammatical (probably).

In 2011, there's probably no "real" natural pronunciation of "an historic". The form probably only occurs as a hypercorrection by people who have seen such forms written down from a previous stage of the language. At one time, the "h" of various words (including "history", "hotel") behaved essentially as in the "h" or "heir" and "hour". Nowadays, they basically don't; the usual, naturally occurring form is "a history", "a historic event", "a hotel" etc. 200 years ago, pronouncing "an 'istoric" rather than "a historic" was probably as natural as saying "a biscuit" rather than "an biscuit" today. But this is no longer the case.

However, a few speakers do in writing ape the previous usage, and this then leads to the "problem" of how to pronounce a form that essantially "doesn't occur" naturally. In practice you will often hear speakers pronounce the "h". As I say, I think the form per se is essentially a hypercorrection, so to ask whether you "should" pronounce the "h" seems to me a meaningless question.