Everyone is entitled to emergency assistance with the public health care system in Iceland.
Iceland has a good public healthcare system which is nearly free for citizens and residents of Iceland, a small fee must be paid for each visit to a Health Clinic, approx. 1200 ISK (~7 Euro). However during your first 6 months in the country you are not a fully-fledged Icelandic citizen, so you must have with you the European Health Insurance Card (EHIC).
See here how to apply for it in your country
If you have lived and worked in an EU/EEA member country for the last 6 months, that time is taken into account for your total 6 months needed. You must obtain form E104 (or E106/E109/E121) from the insurance institution where you last resided.
These forms must be submitted along with the registration form Application for registration at Icelandic Health Insurance.
If you do not speak Icelandic or English you are entitled to an interpreter free of charge, if you need interpretation you should make note of this when making a doctor’s appointment and an interpreter will be booked to accompany you at your doctor’s appointment.
You can also see here for further information about Interpreter Services