Because of the change in activity the eruption area has been closed. We urge people to be careful we it reopens and well-prepared, and stress that you are there on your own, the responsibility is all yours.
The glacier itself (Eyjafjallajökull) and Þórsmörk are no-access zones, and the road up Fimmvörðuháls and Thórsmörk is closed to cars.
You can drive to Skógar, which is perfectly reachable in a normal car, and hike up from there when the eruption site will be reopened. You should register at Skógar so that they know you’re there in case you get into trouble. Expect to take about five hours to reach the top in good conditions — but whether you get good conditions is a total crapshoot. We do see blizzards there in July! Weather up there changes real fast, so dress and pack accordingly.
ICE-SAR has this advice
• Follow the weather report and take it into account.
• Make a travel plan and leave it with friends/family.
• Familiarize yourself with the area.
• Good clothing is of course utterly crucial. Ideally wear several layers of breathable clothing and the outermost layer needs to be waterproof.
• Pack at least a minimal first-aid kit and energy-rich food.
• Good telecommunications equipment is important for safety, and you have to know how to use it. A VHF radio or an NMT phone can make all the difference if something goes wrong, and to be able to notify others of a changed plan.
• A GPS locator and a compass should be standard equipment. And you have to know how to use them.
• A sleeping bag, an insulating mattress and a waterproof outer bag or a small tent can make the difference between life and death if a traveller needs to lie outdoors for some reason.
• It is better to back out in time than to get yourself into real trouble.
Also, if you are carrying expensive and heavy photo gear, make sure you pack it nice and waterproof — and make sure you are ready to carry it all along with your food and other necessities for ten hours.
Can’t blame you, I really want to go there myself! Just make sure you take the place seriously; people have died there in bad weather, even during summer time.