Under normal circumstances the wizard can be moved like any other creature. Wizards are capable of special movements. Firstly, wizards can climb magic trees, enter castles, and ride certain creatures. For conenience these activities are collectively called mounting. You cannot mount if you are engaged, otherwise mounting is effected by simply moving the wizard onto the cell occupied by the entity you wish to mount. There is a bug in the program which currently prevents you from mounting undead creatures.
Dismounting is somewhat more complicated as the computer needs to distinguish which of the two entities is to be moved. For trees and castles the computer will assume the wizard. For ridden creatures the default is the creature, to dismount from a creature the following sequence should occur:
Mounting is generally a good idea, as it hides your wizard from view and gives the wizard additional protection.