My wife and I went to Iceland several years ago on one of he organised group treks that are available. Although normally you end up on a large bus as part of a group of thirty plus, we were lucky and ended up in a small group of only 10 plus driver/guide travelling in a new luxury minibus.
We chose to go in the very first week that the road across the middle of Iceland was likely to become passable - it's blocked due to snow etc for all but 8-10 weeks of the year. Our tour took us from Reykjavik, around the south and western coasts up to Lake Myvatn (pronounced "meeva"), then back across the middle of the island to Thingvellir (pron "thing-kvet-lee") via Landmannalaugar.
On these trips , you camp at organised but still very rustic sites. The tents are provided and are stored at the site so that there is no need for them to be transported. You take your own clothes, sleeping bag and essentials. Food is in a communal mess tent, basic but plentiful and cooked for you. Everyone mucks in with the clean up afterward. We took out own dome tent which anyone is invited to do if they wish. It was a good idea, on one site the weather was so bad that we were up in the night working to stop the big tents provided by the company from being blown flat !
Although there isn't the same freedom on an organised trip, it's important to realise that iceland is a fragile environment with very limited settlements and facilities outside Reykjavic. I would say it's best to go with a guide just to get the most out of the visit. A small group is very much to be preferred. If you are well enough off, hire a 4x4 and driver and make up your own party, but remember that essentially there is one road around the coast and one across the middle, so there isn't a lot of option for exploring "off the beaten track". The track is beaten - full stop ! The guides will show you things you would never find out about on your own - like the best places to go and bathe where hot springs feed into rivers, birds nesting sites (puffins, how to get yourself dive bombed by arctic skuas) and the like.
Also bear in mind that this isn't an entirely trivial exercise if you want to go drive on your own. Only about 10 miles of road on the island are concrete / asphalt. Most of the road is unmetalled and can get swept away by floods and the like. Icelandic 4x4's are specially adapted with high clearance long travel suspension, high level air and exhausts, long range HF radio as well as VHF and cellular etc etc. Our driver - despite plenty of experience managed to drown the engine of our vehicle fording a river with the water level halfway up the doors. We were lucky to get a tow out and three of us then spent a long day working in sub zero conditions to remove the injectors and empty the water out of the engine before we could continue.
On 3 occasions we had to rescue european holidaymakers in unsuitable vehicles who had gone off the road and been bogged down to axles in volcanic dust or careered off the southern highway which for 50 odd miles is just a rough road scraped along the top of a twenty foot high earth bank.
There is a good guidebook to Iceland but I can't remember which one it is because my copy is out on loan and I can't recall who borrowed it ! It's small format, and inch thick, with a red cover and picture on the front. I've bought others from this series including south central France and they're excellent guides.
If you have questions, ask away.
Cheers, Alick
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