I got curious if there was a pronunciation on Wikipedia of “Eyjafjallajökull”, which of course there was. In the really helpful IPA alphabet, which is: “ˈɛɪjaˌfjatlaˌjœːkʏtl̥”. I got about halfway through deciphering this when I gave up.
Fortunately, there’s a recording of a native speaker. Did you catch that? Me neither. Finally, looking on the talk page, there is a great discussion. One useful resource in that section is this clip from ABC News.
So, here’s what I was able to ascertain is the best way to describe it in text. You say: “AY-ya-fyot-lah-yoe-kdl” with a particular emphasis on the “AY-ya” part to distinguish it from all of the other silly fyot-lah-yoe-kdls (mountain glaciers) that they have a million of in Iceland.
According to the New York Times blog, if you’re a native English speaker, your best chance of saying this is to mumble “Hey ya forgot the yogurt”. They’ve also got perhaps better text versions of how to say it.