Where to go?
For first timers like myself I would suggest July-August. Not because of summerly temperatures but because several highland roads open only in June-July. Without these you will only see half of Iceland or less. In later months the weather gets progerssively worse and days become shorter and shorter
What's the weather like?
You won't sweat, that's for sure. Expect 5-20 C at the most in July-August, 20 C being very warm. It has to be said that weather can change very quickly, including sunshine, rain and wind. Prepare yourself with rain and wind resistant clothes from head to toe.
Where to go?
For me Iceland is all about nature. es, there are cities and churches and nice buildings but if that's what you are looking for go somewhere else. If you make the trip to Iceland it makes sense to do more than 1 day trips from Reykjavik to overvrowded tourist locations. A long week and driving around Ring Road (Road No. 1) will show you much more and you can make detours as you like. Just open your eyes and read my blog :)
Where not to go?
Keep in mind that if you rent a normal 2wd car you are not allowed to drive on roads which have an "F" before their number roads. If you rent a 4wd with a bit more clearance you can go anywhere you like. Legally at least. Fording rivers can be tricky and any damage while doing so is not covered in your insurance. Be well informed and keep in mind that rivers can vary in depth day by day. To sum up, F roads are only for 4wd cars (jeeps) and always take good care with rivers and sandy/muddy roads (not to get stuck).
It didn't take me long to realize we needed a 4wd for our purposes. I went through about a dozen of websites and I am happy to recommend http://www.iceland-car-rental.com/ where we ended up renting a Nissan Terrano II. They were relatively cheap and provided all the necessary insurance without extra costs. The car itself while not brand new and not in the leagur of Land Rovers and Land Cruisers, was perfectly fine for us and managed all the rough road we threw at it.
This was the one that took me the most time, finding the right accomodation for the right price, fitting into our tour schedule. But ince again Google earth and just plain old Google came to the rescue and managed to book accomodation for between 30-50 EUR/night/person which while surely not cheap compared to about anywhere else in the world was still acceptable. This gets you basic, clean double bedrooms with breakfast and shared bathroom. What I did was avoiding time and money wasting booking agencies and contacted the accomodation itself.
Money, money, money
Iceland is an expensive country, especially if you use anything where domestic human hand is involved ie. services. Going out dining is not for the faint hearted. But no problem, breakfast was included for every accomodation so we ate all there was to our liking, made some sandwhiched during the days and brought along our own food for dinner from home and prepared it in the little kitchen corners or twice we paid for dinner at the accomodation. Apart from gasoline and food we didn't pay for anything.
http://www.road.is/ - road and weather conditions, webcams
en.ja.is/kort - a very-very good map
http://www.osm.org/ - another map, much better than Google Maps, even show some hiking routes.
www.loftmyndir.is/k/kortasja.asp?client=vatnajokull - one more map, best satellite maps but not for the whole country
www.tripadvisor.com/ShowForum-g189952-i223-Iceland.html - there are some good topics and many silly topics as well
http://www.isafold.de/ - this German guy spent like ten summers hiking all alone in desolate places where I guess not many people have gone before - amazing
Apart from these: use Google Earth, Google and Youtube.