Again this is partially taken from the textbook I’m writing, so I’d really appreciate if something is wrong or not understandable. Here are the letters currently in the Icelandic alphabet. The chart is sorted by: letter, both capitalized and lowercase / How the letter is spelled in Icelandic / How to pronounce the letter name in English (approximate) / The sound the letter makes in English (approximate).

(1) These two th sounds are different. Ð is when your tongue is vibrating and þ is without vibration.
(2) Purse your lips (this is what “with rounded lips” means) as if whistling or kissing, instead of the slacker lips in English.
(3) My teacher described older people as more often saying “echs” whereas younger people usually say it the same as in English. A book about Icelandic for Icelanders from the 1930’s described x being pronounced as “egs”, which seems like the closest-sounding alternative to the English x.
(4) Also the o in worker, u in murder, and “e as in set with rounded lips”. This does not exist in English and varies in sound depending on the word being spoken and the speaker, so sometimes it sounds like a genuine ö and sometimes it sounds much more like e. I was taught that your tongue is in the exact same place as when making the e sound (as in bed, bet, first e in meddle), and the only difference is that your lips are rounded. This is a sound that may be easier for English speakers to mimic than say on its own.

Other letters:

* Since the letters c and q don’t exist in Icelandic, according to one person they’ll be pronounced the same as in the foreign word’s original language (or q at least will be pronounced as k). “Celcius” would have the c pronounced as an s, for example, and people don’t tend to pronounce it in a single way when they don’t know how it is in the original language. However I’ve never heard anyone else say this and so if you know anything, please let me know.

There are some things called “diphthongs / tvíhljóð”  that are two vowels next to each other. These are au (sounds like the Icelandic öi, but since ö can range in sound it may sound similar to ey/ei) and ey/ei (sounds like ey in hey). When spelling something, diphthongs aren’t spelled out, but are just pronounced instead. You wouldn’t spell au as a and u (like “ah, uh”) but as au (“öi”). Au’s name is the same as its pronunciation but ey’s name is ufsilon ey / tvöfalt ey and ei’s name is einfalt ei.

Einar – Ei, enn, ah, err. If you’re spelling an Icelandic word you don’t have to spell out the diphthong, but if spelling a foreign word it’s best to spell it out.
Auður – Öi, eth, uh, err.
Caffeine – Syeh (sé), ah, eff, eff, eh, ih, enn, eh.
When spelling a .is web address, you usually just say “is”as if it were a word instead of “ih ess”.

Other useful things:

The book “Íslensk táknaheiti” covers every (or almost every) symbol your keyboard can make and I happen to own it (you can also buy it at the University of Iceland’s bookstore, not sure where else), so if you want to know what other symbols are in Icelandic just let me know.

The “…-merki” might not always be said, in class we just say “hjá” instead of “hjá-merki” when spelling our Email addresses.

I thought there was an Icelandic name for “www” but if so I forgot it. If you know it, can you comment and tell me?