The official coronation of Solomon reached its peak through the physical and symbolic act of anointing with oil, accompanied by the public declaration of the people. Zadok the priest used a receptacle shaped like a horn [מצודת ציון] to perform this sacred task. This horn contained the exact amount of special anointing oil required for a royal coronation. In fact, [רש"י] notes that this was the very same original anointing oil prepared by Moses in the desert.
The exact location from which this sacred oil was retrieved is a matter of discussion. The primary approach among commentators is that the oil was kept in the tent David pitched in the City of David in Jerusalem, which housed the Ark of God. According to this view, the flask of anointing oil was permanently stored right in front of the Ark. On the other hand, [רד"ק] suggests that the oil was retrieved from the original Tabernacle, which was located in Gibeon at that time. He explains that when the Ark was previously taken into battle against the Philistines, the anointing oil and the jar of manna were left behind in the Tabernacle and did not travel with the Ark to Jerusalem. Consequently, Zadok would have needed to travel or send a messenger to Gibeon to obtain the oil. While [רד"ק] acknowledges the possibility that the oil had been brought to Jerusalem and placed before the Ark, he concludes it is more likely that these sacred objects were never removed from the Tabernacle until the permanent Temple was built.
The physical act of anointing followed a specific procedure. As brought by [רד"ק], one approach describes the oil being poured first on Solomon's head, followed by an application between his eyelashes in the shape of a crown. Another perspective argues for the reverse order, suggesting the oil was first applied between his eyelashes, with the remainder in the horn then poured over his head.
This initial anointing, celebrated with the sounding of the shofar and the joyous cries of the crowd, took place solely in the presence of the residents of Jerusalem. Because of this limited attendance, [רד"ק] explains that Solomon was anointed a second time at a later date. This subsequent ceremony was a massive public event. David gathered all the leaders of Israel and the tribal representatives to Jerusalem, where Solomon was publicly anointed as ruler before the entire assembly. Alongside him, Zadok was also anointed as High Priest in a grand celebration marked by immense joy and the offering of many sacrifices.