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General
Much of the time one is walking on 4WD tracks or trails which are generally easy to follow. When going cross country you are generally walking to a specific spot you have chosen (in other words you are walking on a bearing for a specific distance). So you'll have a compass of some sort. One of the beauties of making your own trail is... you can't lose it!

Tip of the day!
This caught me out. I am in Iceland in July. It is near midnight. There is a beautiful sunset. I am walking with the sun to my left. Which way am I heading? No, not North, I am heading East. Because the sun in summer sets (if sets at all) near enough in the North. And of course it rises there as well. So that is something to bear in mind. The sun is still in the South at midday of course.

GPS
My GPS was in use often, but much more to record and to check progress than to find out where I was. I recorded waypoints every so often and also had auto track recording turned on (a point every 20 seconds). This was to create, eventually, a trail map.
On the second last day in the clouds with no visible markers everyone else was obliged to follow me across the snowfields, as I was the only one who knew where we should be heading. 'nuff said.

Compass
I had a compass which was not used much or very good. To be fair it was bought in NZ and balanced for that region. 
Note to self: Get a global needle compass! 
There is also an electronic compass on my watch. 
However I find it a good practice to walk to a bearing and estimate distances manually. It is a skill well worth developing and maintaining. Then check with a GPS to see how accurate you are.
Estimating distances here is quite hard. I often thought that a bus-sized rock was 2km away. 200m later I would pass a boulder the size of a TV set. This happened often. I am not sure why. Maybe it simply takes time to get accustomed to a new landscape. Maybe the mist made things seem further away.

Altimeter
I hardly ever checked the altimeter as it is a largely flat walk (especially when coming from Nepal!).

Map
For planning purposes I visited the best map shop in the world which is Stanfords in Long Acre (Covent Garden, London). I bought a German tear-proof, water-proof map of the whole of Iceland for 10 quid. And it is pretty.

GPS Map
A free topo map for the whole of Iceland is available here. Pretty much covers all you'd need.
I will cover other GPS related resources elsewhere.