Often referred to as iceland's highest waterfall, Glymur is technically only the second highest. However the highest waterfall is in such an obscure location that most tourist organisations found it better that Glymur should be number one. That being said, the Glymur hike is very high on my list of best hikes in iceland and a must if you're in the area.
About the trail
Take a closer look at the map to find the start of the hike. The parking can be found by taking an paved road next to a street called Hvalfjarðarvegur. This is quite a long street so it's best to keep a close eye on your map. At the start you'll find an abandoned house. You can explore this at your own risk as a lot of the interior is rotten. Be prepared for some creepiness. A bit further you'll follow the path steeply upriver. All along the way you'll have great views into the ravine next to you. At the top of the waterfall you have to cross the river. If you are uncertain of yourself it might be better to go back the way you came. In any case, carrying a pair of watershoes or sandals might be helpful here. Leave the beltbuckle of your backpack unclipped and be ready to drop it if you would fall. After the crossing you go downhill on the other side of the river, back to the parking.