Possibly the number one question we're asked when it comes to planning a trip to Iceland. Why not? They look incredible and the fact that you're not guaranteed to see them makes it all the more exciting to go out on the hunt, at least I think so!
There are a few criteria required for viewing:
1. Right time of year.
They seem to be less common during the summer months in the Northern Hemisphere, this might have to do with angle of the planet against the sun and those forces interacting with our atmosphere. Iceland is pretty far north and might be subject to some further extreme of this effect.
2. Right time of year for darkness.
It needs to be dark to view them, for Iceland that's during the months preceding and following winter solstice (21st of December) - the shortest day of the year for most of us on this top half of the planet.
You'll have the best chance of dark skies starting about the end of August and right through to maybe early April. Bearing in mind that the night gets longer from September through December and then shorter again from the end of December through to April during this period. You might expect a longer night to offer more opportunities!
3. Clear skies.
The phenomena occurs in the earth's atmosphere, if there are clouds or overcast skies you will not be able to view anything. This can make it exceedingly difficult to plan your adventure far in advance as weather forecasting can't be relied upon further than a few days in advance. Most excursions are confirmed in the last 48-72 hours.
4. Low levels of light pollution.
The further from city life you can get, the better. Street lights, billboards, traffic, etc., all add to the din of surface light which will reduce or obscure the light show which could very much be occurring above your head.
In summary, autumn might be the most comfortable time in balancing the weather, surface temperatures, and conditions of darkness to view the aurora borealis.