* BYAR-nee HER-yoolfs-son
Here's a breakdown:
* Bjarni: "BYAR-nee" with a short "I" sound like in "bit"
* Herjulfsson: "HER-yoolfs-son" with the "j" sound like the "y" in "yes" and the "u" sound like the "oo" in "moon".
You can find some online pronunciation guides for Icelandic names, or even listen to recordings of Icelandic people pronouncing the name.