The Arkenhammer resembles a brightly-colored plastic toy hammer. It is about the size of an Erfworld-scale sledge hammer. When its powers are used, it is surrounded by the sparkling light effects typical of Erfworld magic.
The Arkenhammer enables Stanley to tame dwagons. According to Ansom, tamed dwagons will defend Stanley to the death while he wields the Arkenhammer. It also enables Stanley to fly (at least sufficiently to rendezvous with an airborne dwagon). As an artifact, it presumably gives its wielder a substantial combat bonus. It can also turn walnuts into pigeons. Presumably these turn back after a few turns, a la Bogroll's pigeon pie.
It is unknown what powers the Arkenhammer would manifest to a non-attuned wielder.
While serving as a warlord in the service of King Saline IV, Stanley found the Arkenhammer. It attuned to him. With the aid of his tamed dwagons, he won a number of battles, which earned him the esteem of King Saline. As a result, he was promoted to Chief Warlord and made Saline's Heir Designate.
Stanley interprets all this as proof that he has been specially favored by the Titans, and that it is his destiny to control the Arkentools. Specifically, he believes that Prince Ansom, who wields the Arkenpliers but is not attuned to it, marched on Gobwin Knob as part of a divinely ordained plan to bring the Arkenpliers to him.