These magic users carry magical staffs with them some or most of the time, which are used to concentrate their magical energy. They usually use verbal spells but point their staff to charge the energy. Their eyes aren't seen glowing gold, suggesting they practice magic in a different way from e.g. Merlin, Morgana or Morgause, who use spells mainly by just concentrating the power with their eyes, hands or head movements. Merlin has shown ability with a staff but the extent to what he can perform with the staff is unknown. He only used the staff in emergency situations- for example, destroying the Sidhe elder who hunted him in The Changeling and destroying Sophia and Aulfric in the Lake of Avalon.
The Cailleach holds a staff all the time, and has not been seen putting it down, but it's unknown whether she uses this to concentrate all her energy, considering she is a goddess. Although when Gwaine attempted to attack her, she looked at him tensely and her eyes glowed a light gold/white colour, with a small hand movement, but it is likely this was not necessary and only by reflex.
Morgana used a staff once, the Rowan staff, to awaken the living dead in order to defeat the knights of Camelot during the great battle for Camelot in Series 3. The staff was carved from the Rowan tree, but Morgana only appeared to hold it once, when it smashed into the ground, and after that it was left to stand alone. Merlin later destroyed it after a sword duel with Morgana.