By road
Hitchhiking is a cheap way of getting around in Iceland. The country is among the safest in the world, people are quite friendly and the percentage of drivers who do give rides is high, especially in the off-season. However, low traffic in areas outside Reykjavik makes hitchhiking in Iceland an endurance challenge. Even on the main ring-road the frequency of cars is often less than one car per hour in the east. Nearly everybody speaks English and most drivers are interested in conversations.
Avoid hitching after nightfall, especially on Friday and Saturday night. Alcohol consumption is high and alcohol-related accidents are not uncommon.
Hitchhiking into the interior is tough, but everything works if you have enough time - calculating in days, not in hours. For longer distances or less touristic areas be prepared with some food, water and a tent or similar. The weather can be awful and sometimes spoils the fun of this way of travelling.
The HitchWiki website (http://hitchwiki.org/maps/) has some advice for hitchhikers.
By plane
Aircraft in Iceland are like buses or trains elsewhere - they're the main form of internal travel other than the roads. Be warned though, that the ride can be a bit bumpy if you're entering one of the fjords like Akureyri.
Scheduled service to nearby destinations, including Greenland and Faroe Islands, is provided by Air Iceland (http://www.airiceland.is) and Atlantic Airways (https://www.atlantic.fo).
By car
A car offers the most flexibility for travel around Iceland. Numerous agencies rent vehicles, and ferries allow individuals to bring their own car with them. Rental prices are high - expect to pay at least ISK4000 per day for a two wheel drive vehicle, and upwards of ISK12,000 per day for a four-wheel drive vehicle; these prices include basic car insurance, but additional insurance may be purchased to protect against damage from gravel or other common mishaps. Read the fine-print however, because the things that usually break windshield, tires, bottom of the car are usually excluded. Travelers can see the majority of Iceland's sights with a two-wheel drive vehicle, but those interested in venturing into the interior or to places such as Landmannalaugar will need four-wheel drive - and long experience at the wheel - as roads are rough and rivers may need to be crossed. In some locations it's best not to travel alone due to the difficult terrain and weather conditions. Be aware that renting a four wheel drive vehicle may require reservations made several months in advance as these vehicles are in high demand. In addition, renting cars on-location is almost never cheaper than doing so in advance, and car rentals, including at the airport, are not open around the clock.
Driving in Iceland is on the right side of the road. Headlights and seat belts for all passengers must be on at all times. There is one main highway, Route 1-Ring Road, that encircles the country.
Gas can generally be obtained 24 hours at self-service stations using a charge or credit card, but you will need a personal identification number for that card. Alternatively, most stations sell prepaid cards that can be used to buy gas after-hours. If traveling around the country, the gas tank should be kept near full because stations can be 100-200 km 62 to 124 mi apart. Petrol costs as of summer 2011 are around ISK240 per litre. Because of Iceland's ever-changing weather, one should keep extra food and know where guesthouses/hotels are located in case of a road closure.
Most mountain roads are closed until the end of June, or even longer because of wet and muddy conditions which make them totally impassable. When these roads are opened for traffic many of them can only be negotiated by four wheel drive vehicles. The roads requiring four wheel drive and possibly snow tires are route numbers with an "F" prefix, e.g. F128. The general speed limit on Icelandic rural roads is 90 km/h on paved surface and 80 km/h on gravel, in urban areas the general speed limit is 50 km/h. There are some exceptions from the general limits that are specifically signed as such the limit is never higher than 90 though but be aware that the general speed limit is usually not indicated by signs. Speed cameras are posted around the country, and fines can easily reach ISK 50,000 - 130,000. The DUI limit is 0.05%, with a minimum fine of ISK 70,000 - don't drink and drive.
Drivers in Iceland should familiarize themselves with road signs and be prepared for Iceland's unique driving conditions. The roads in Iceland are of a high quality, typically made from slightly rough black basalt. Crossing rivers can be very dangerous, particularly if it has been raining, and should be done with great caution. Driving on gravel can be a challenge, and loss of control on cliff-side roads can easily be fatal. There are two signs in particular that foreigners should pay attention to. First, "malbik endar" means that the road changes from a paved road to a gravel road. Slow down before these changes, for one can lose control easily. Also "einbreið brú" means that a one-lane bridge is approaching. Arrive at the bridge slowly and assess the situation. If another car has arrived at the bridge first allow them the right of way.
If you are traveling by road a great site to check is the Iceland Meteorological Office (http://www.vedur.is/english/) who have an excellent set of pages including the Icelandic Road Administration (http://www.vegagerdin.is/...) on all of the main roads.
There are no road tolls on Icelandic roads, except from the Hvalfjardargong tunnel located approx. 30km north of Reykjavik. For vehicles up to 6 metres, the price is ISK 900, 6-8 metre vehicles pay ISK 1200 and drivers of larger vehicles than 8 metres pay ISK 2300.
By bike
Cycling is a good way to experience Iceland, and provides a very different experience to other means of transport. You should bring your own touring bike, as buying a bike locally can be expensive. Traffic in and out of ReykjavÃk is heavy, otherwise, it's OK. You can cycle safely on the Ring Road, or take the bike on the buses which are equipped with bicycle racks serving the Ring Road and do side trips. However, if going self-supported, considering the weather and conditions, it is strongly advisable to have a previous touring experience.