ApproachFrom Herðubreiðarlindir you have two options. You can either do a long hike to get there that goes around the mountain to the other side, or, if you have a decent 4WD vehicle with good clearance you can drive to the base of the climb.
First of all, it's long. There was no distance given but I would estimate it at about 7 to 10 miles one way. From the campsite, cross the creek and follow the yellow posts west towards the mountain. It crosses a lava bed for a mile or two. Up and down, up and down through the lava until you break free near the base of the scree. Actually, the posts go all the way up to the scree and then turn right (north) and simply walk on the flat ground around the whole mountain. It's frustrating as you think they would have made a more direct route from the campsite instead of all the way in and then around. The hike takes at least 3 hours of steady good-paced hiking to reach the sign at the base of the climb. Enjoy.
From Herðubreiðarlindir, drive south of F88 approximately 12 kilometers to a small sign pointing west that says Herðubreið. Turn right here and follow it in another 12 kilometers or so to the base of the climb. I did not drive this in but the warden says it is pretty rough. But, if you can manage it, I would recommend it. The hike in is just stupid and long. Save yourself the aggravation. And even if you can not make it in the whole way, you will save yourself at least part of the hike in.
Route DescriptionFrom the base of the climb, head up the rightmost scree mound you are facing on its leftmost side. You will pick up a trail that does short switchbacks up the scree. Above the soft scree, the ground will harden under your feet but still be covered by rocks just before you get to the breach in the cliffs. Go through the breach where the snowfield comes through but stay as far left as you can. Once through the breach the route will angle left up the least steep way until you crest the lip of the rocks. Look right and follow cairns across the plateau atop Herðubreið. They will cross snowfields and lava flows to the summit cone. Ascend third class rock on the southwest side. The way is clear. Descend the same route.
The route is approximately 14 to 20 miles long round trip with 4200 feet of elevation gain.