In old Icelandic a lot of words were written without a u before an r but they were still pronounced as far as I can tell as if they had one. So the current Icelandic word for ghost, or "draugur" should sounds the same as "draugr". I don't think it's really possible to find a representation of the "au" sound in English but else it is pretty straight forward "Dr-au-g-ur" (ur like in Dagoth Ur).
I found this after a quick google search.
au like the vowel in french "feuille", similar to "oy" in "boy" but I don't know if it can be trusted, the "oy" in boy doesn't really represent the "au" sound properly and I have no knowledge about french
but perhaps this text can be of help.
Would probably be easier to just record the word and upload it somewhere... however it seems Bethesda isn't really pronouncing "Draugr" the same way Nordic countries would in the game anyway so there may as well be a different pronunciation on Nirn than IRL, but seeing the whole nordic theme of Skyrim I take it they were going for Nordic languages and pronunciations.
"This" only goes so far when it's 100% correct/accurate. If we go by Nordic pronunciations of the word then "Drow" (as said in D&D) is far from the start of the word "Draugr" and "gur" doesn't really sound the same in English as in Nordic languages (at least in Icelandic) since there is an emphasis on the "u" in "gur" so there is like a short pause after the "g" and the "u" is said louder in comparison to English, like "g-Ur".