The walking track to the top of Útigönguhöfði starts right behind the Básar hut. The route follows the ridge above the huts to the Votupallar plateau, before leading up the steep & craggy slope of Útigönguhöfði itself. This is also where you emerge from the Hvannárgil canyon on the way back.
On the signpost you will see two different paths to Útigönguhöfði, but eventually they both lead to Votupallar. The lookout point on the edge of the plateau offers amazing views into the Hvannárgil canyon