Learn Icelandic: Takk fyrir kaffið! - Thanks for the coffee!

In Icelandic, the word for "the" isn't a separate word before the noun; it is added to the end as a suffix. Kaffi is a neuter noun meaning "coffee," and adding -ð makes it kaffið ("the coffee").

Does the preposition fyrir change the ending of kaffið here?

It does, but you can't see it! Prepositions in Icelandic force the following noun into a specific grammatical case. When fyrir means "for" (like thanking someone for something), it triggers the accusative case. Luckily, kaffi is a neuter noun, and neuter words look exactly the same in the accusative case as they do in the dictionary.

Is this a common phrase to use in Iceland?

Absolutely. It is a very strong cultural habit in Iceland to thank your host or whoever treated you to a drink or meal. Just like you would say Takk fyrir matinn (Thanks for the food) after dinner, you say Takk fyrir kaffið to the person who made or bought you coffee.