Clear all shelves completely so you can access the shelving unit from any angle.
Examine the shelving unit from top to bottom, noting connection points between the shelves and the body of the unit as you inspect. Look for structural braces in the unit--areas where metal reinforcement brackets keep the unit in a single piece, rather than shelving connections meant only as shelf support.
Remove the shelves supported only by pegs or ledges extending from the shelving unit's side. Slide the shelves from the body of the unit and set them aside. Remove the pegs from the holes in the inside walls of the shelving unit by hand, or use a pair of pliers if the pegs prove difficult to remove. Unscrew support ledges secured to the interior unit sides that held the shelves in position using a Phillips-head screwdriver. Then remove the ledge pieces from the unit.
Unscrew the metal brackets that hold structural shelve pieces in place. Structural shelves are the individual shelves throughout the unit that help the unit hold its shape. Have someone hold the shelves as you unscrew the brackets from the walls of the unit. Pull the shelf from the unit, and then unscrew the brackets from the shelves themselves.
Remove the rest of the screws holding the main frame of the shelving unit together. The pieces held in place by the screws include the top and bottom pieces of the shelving unit, as well as the unit rear board. Begin with the top piece, followed by the rear board, and then finish by unscrewing the two side pieces form the unit base.