I myself have never witnessed a Psyduck in the wild. I was, however, lucky enough to witness the episode where Misty acquires her Psyduck (see Who is Misty?) and thus have had a rare glimpse of Psyduck behavior outside of the pokeball (small, red and white balls used for Pokémon storage). Basically, Psyduck stood there looking vacant. This, it seems, is normal Psyduck behavior. In addition, they frequently clutch their throbbing heads.
Of course, Psyduck is most at home in the pokearena, which may be a word I just made up. Alas, I have only seen a few brief moments of Psyduck in combat, but some day each attack will be followed by a short description.
Normal Attacks*UPDATE!* Due to the tireless research of your humble narrator, you may know click the names of certain attacks above to view those short descriptions I promised back before this page was even posted.ScratchPsychic Attacks
Fury SwipesConfusionWater AttacksHydro Pump
In those few breif moments of combat, the Psyduck redirected a jet of water from a hostile Staryu up into the air and back upon the Staryu, who was unable to continue fighting. This awesome display of psychic powers is no doubt only a small glimpse at Psyduck's full potential.