Remove the drywall from both faces of the partition wall. Knock a hole through the face of the drywall with a sledgehammer or crowbar. When you locate the edge of a sheet of drywall, work the crowbar underneath the edge and pry it off.
Cut the nails or screws that are connecting the bottoms of the studs to the base plate by cutting between the two with a reciprocating saw. Pull the bottom of the stud out and away from the wall and pry it off of the top plate. Use this method to remove all the studs.
Pry the base plate up off of the floor using the crowbar.
Pry the top plates off of the ceiling using the crowbar. On a vaulted ceiling, there will be two top plates rather than one, but they are both removed in the same way.