June, July and August are the best times for weather in Iceland. It is the Tourist season. In the fall, spring and winter things are cheaper but
The duration of your stay depends a lot on what you want to see and do. For just Reykjavík, the Golden Circle and the Blue Lagoon, which is the basic tour you would need half a week to a week, and if you want to see more of the country I would suggest two weeks at last.
For the basics, if you arrive or depart in the daytime, you can incorporate the Blue lagoon trip into that, because it is on the way to Reykjavík from the airport. Or you can go at any time and then should recon for a half a day at least. It's realy nice though so it's best to have the rest of the day open, just in case. Or do some things before.
There are many company's that offer a trip for the Golden Circle, which includes Thingvellir our most historical location, Geysir, the geyser all the other once are named after, and Gullfoss a magnificant waterfall. The Golden Circle takes a day.
Reykjavík is our capital and I would take about three days to explore that at least. For the main party time, friday and sathurday are the days. In June we have our national holiday on the 17th if you want to include that.
For traveling the rest of the country, I have this to say. There are many interesting places to go to, and the whole circle can be driven in three days if no stops are made. If however you want to enjoy it I'd take a week or two for the country side. If you want to wisit just one of the four quarters though you can do that in two to three days. To travel by car to the other end of Iceland is about eight days in a solid drive. In any case you can recon for one day for the trip to wherever you want to go, and one day back. Iceland is quite expencive to travel in but with the right planing it can be done. You should order a rented car now if you want to use one, or you can take busses or go by air. Air travel, busses and rental cars are all expensive, you will have to check out the best way, taking in what you want to get out of the trip.
Food is expensive in Iceland, but there are low cost stores, and by buying there instead of in the roadside shops can cut the cost of food in half at least.
Hitchhike along the southeast coast and you will see glaciers, mountains, lavafields and waterfall. If you have time, do the Skogar-Thorsmörk-Landmannalaugar trek on the way.