As the typical advertisement for a PhD student position has some statement like "salary according to wages contract", an applicant does not know what this means in practise for the salary to expect.

Currently, the union responsible for PhD students at University of Iceland is Félag háskólakennara / Association of University Teachers. They made a contract with University of Iceland. For the latest version, check for Stofnanasamningur Fh og HÍ. In the version from 5. March 2021, you find in Section 4.3 that PhD students (doktorsnemar) get salary level 030. The first two digits are the y axis in the salary table and the last digit is the x axis.

There are two salary tables, one for academic staff, i.e. those who have a PhD ("A 696") and another one for administrative staff ("S 695") -- note that these cryptic numbers are sometimes used a pre-fix in front of the salary level, e.g. "695 030". As PhD students have not yet a PhD degree, rather the non-academic, i.e. the administrative staff salary table applies, so you need to look at Launatafla stjórnsýslu.

The most recent salary table is from 1. April 2023. Take care to have in that spreadsheet the tab "Mánaðarlaun" opened to get the monthly salary. There, you will find that salary level 030 gives you 462 586 kr. per month (as of 1. April 2023.). This is before taxes, so feeding this into a tax calculator gives 361 867 kr. after taxes (as of the tax system valid at time of writing, i.e. 2023).

P.S.: As postdoc (Icelandic term: nýdoktor), the academic salary table applies and you have at least salary level 061 (which is 662 090 kr. in the salary table at time of writing). But for academic staff, in fact an evaluation system applies where the salary depends on the amount of publications that you accumulated over your life. Each publication gives points (for details do a web search for "Evaluation System for Public Higher Education Institutions") and the Table 2.3 in the Stofnanasamningur Fh og HÍ shows a mapping of points to salary levels. While if your PhD is 5 years or longer ago, your are not called a postdoctoral fellow anymore, but a research specialist, but this alone does not increase your salary level.