From the parking lot you start by going through a gate and climb up a flight of stairs. Then there is gravel trail for the next 1km, moderately steep, but not very difficult. Half the way up, around 1,2km from the parking, you will see the Litlanesfoss with all the beautiful basalt columns. There are trails down into the canyon below the waterfall but they are steep and in lose gravel, so it is better to be careful if you decide to enter the canyon.
The next 1km is with winding trails, which visitor's feet have hammered into the soil through the decades. Some parts go very close to the canyon with the danger of fall. So be aware of that, especially if you are accompanied by children.
Continuing your hike you may expect, especially in springtime, to wade small creeks that have left their bed, because of melting snow. When you get to an information sign about 2.2km from the parking lot you will have a clear view to the waterfall and the gorge. To continue up into the gorge can be dangerous, varying on the time of your visit. In winter it can be really icy when you enter the gorge and no secure trail into it. In summertime the trail can be muddy and then you will have to cross the river if you want to go all the way to the waterfall. So be aware of the amount of water that is in the river.
But the hike to the base of the falls terminates in a desolate cove with the roar of the water echoing off the geologically fascinating and colorful cliffs.
For walking back down to the parking lot the easiest way is to return on the same trail on the south side of the river. But you can also, if you have already crossed the river, walk down on the other side of the river (north side) but there are no clear paths on that side. If you are a real climber you can also walk to the top of the waterfall and cross the river up there, then walk down on the other side. But be aware of not getting to close to the great gorge and don't cross the river at the edge of the waterfall. These routes are not marked and all paths quite unclear.
There are several GPS routes to be found on the web for hiking to Hengifoss. You can for example use this one from wikiloc.com: