Target a suitable spot for your storage rack. It should be clear of any obstructions and easily accessed from the attic's pull-down stairs.
Cut four pieces of 2-inch by 4-inch lumber to 48 inches in length.with a circular saw. Place one of the pieces of lumber vertically against the outside edge of one of the joists in the attic floor, overlapping the joist by 6 inches. You will need to push the insulation to the side to place the board. Wear work gloves when you do this to avoid skin irritation. Check with a level that the board is plumb and nail it to the joist with 10d nails at the at the top and bottom of the overlap.
Place the next piece of lumber vertically on the same joist, 12 inches away from the first piece of lumber, measuring from the nearest edges of the lumber. Nail it to the joist. You'll now have two upright pieces of wood; these form one side of the storage rack.
Nail two more pieces of lumber to the outside edges of the second joist over from the first joist, placing the lumber so the four uprights describe a rectangle.
Cut six pieces of 2-inch by 4-inch lumber, each measuring 16 inches in length. Nail the 2-by-4s to the uprights on the inside edges, extending from the front upright to the back to form crosspieces. Place the lowest crosspiece 4 inches above the joist, the second crosspiece 20 inches above the joist and the third crosspiece even with top of the uprights. Do this on both sides of the structure.
Cut three pieces of 1/2-inch plywood, each measuring 16 inches by the width of the structure when measured from the inside edges of the uprights. Lay the cut pieces of plywood between the uprights, resting on the crosspieces. Nail the plywood to the crosspieces with 6d finishing nails.