It takes around two days to hike the straightforward 35km route from Ásbyrgi down the west side of the gorge to Dettifoss, with an overnight stop along the way at Vesturdalur (alternatively, the day-return hike to Vesturdalur makes a good trip in itself). Take a tent, cooking gear and all supplies with you; in summer, SBA (wsba.is) runs a daily Mývatn–Dettifoss bus, so you could arrange to arrive or move on from here.
The trailhead is signposted behind Ásbyrgi’s National Parks Visitor Centre, soon climbing along the clifftop to exit tight birch scrub onto open heathland; 3.8km from camp will find you looking north from the rounded rocks atop of Ásbyrgi. There are two trails to Vesturdalur from here; one short-cuts south (8.5km) but for a fuller view of the gorge, take the longer track (11.5km). This crosses east over the heath for a couple of kilometres to the brink of the gorge, where jutting rocks offer a good perch for looking down at the grey river rushing smoothly across a shingle bed. The trail now follows the gorge south, via intermittent sections of green heath and dark basalt, joining up with the short cut from Ásbyrgi and then entering a brief, slow section of ashy sand. Once through this, a side track makes the short climb to Rauðhólar, the remains of a scoria cone whose vivid red, yellow and black gravel is a shock after the recently monochrome backdrop. Past here you descend to Hjóðaklettar, where the noise of the river – which funnels violently through a constriction at this point – is distorted by hexagonal-columned hollows in huge, shattered cliffs. The Vesturdalur campsite is a couple more kilometres away.
Over the next 8km, the trail moves above the river and then down to the marshy Hólmatungur, where underground springs pool up to create three short rivers which flow quickly into the Jökulsá through some thick vegetation. The trail crosses the largest of these tributaries, the Hólmá, on a bridge just above where it tumbles into the main river. Upstream from here on the Jökulsá’s east bank, the prominent face of Vígabjarg marks where the formerly mighty Vígarbjargfoss ripped through a narrow gorge, before a change in the river’s course dried it to a trickle. From here it’s another 8km to the 27m-high Hafragilsfoss, an aesthetically pleasing set of falls whose path through a row of volcanic craters has exposed more springs, which mix their clear waters with the Jökulsá’s muddier glacial flood (there’s a particularly good view of Hafragilsfoss off Route 864, on the eastern side of the gorge).
A final tricky couple of kilometres of scrambling brings you to Dettifoss and the sealed road south to the Ringroad; if you’re not catching the bus straight away, there’s a basic campsite nearby.