The majority of a wizard's power is tied up in their staffs, which they use to store spells and absorb magic from other sources. A wizard always know where their staff is, even when it's been put in an out-of-the-way location. Wizards' staffs are nearly indestructible, as not even dragon's fire will burn or break them. However, they have been broken by elf or fire-witch magic, or by the Sword of the Enchanted Forest.
Even without their staffs, wizards are not powerless, as they tend to carry a few ready-made spells outside them in case of emergencies.
It is very hard to eliminate a wizard for good. The only known permanent way of getting rid of a wizard is for a dragon to eat them.
Three temporary methods of eliminating a wizard have been shown in the series. First, in Dealing with Dragons, the princess Alianora, captive of the dragon Woraug, inadvertently discovered that wizards could be melted by dumping soapy water with lemon juice in it over them. Second, by the time of Calling on Dragons, the magician Telemain had developed a spell that achieved the same effect. He was able to give Cimorene, Mendanbar and Morwen the ability to perform the same spell. Finally, in Talking to Dragons, one of the Darkmorning Elves was able to dispose of a wizard in an unexplained manner, which also cut his staff into three pieces. In all cases, the wizard would return in a few days.