Remove the screws from the stair tread frame. These are typically found on the bottom or edge of the metal tray, and will usually have Phillips heads. Use a cordless drill for quick removal. Lift the tread from the frame and flip it over to expose the plywood bottom. If there are screws, the two pieces can probably be separated; if not, you will need to cut a new base from 3/4-inch plywood.
Separate the tread from its base if possible. If it cannot be separated, set a piece of 3/4-inch plywood, a little larger in all directions than the tread, on top of the tread frame so that it extends past the edge of the frame in all directions. Trace the inside of the tray's top edge onto the plywood from underneath with a pencil. Cut this piece out with a jigsaw and use it as a template to make as many bases as you have steps.
Remove the carpet from the tread top. Remove the staples from the bottom edge with a pry bar. Loosen any glue holding the carpet with a chisel. Set this piece on a sheet of 3/8 plywood and mark its outline. Repeat for each step.
Lay out enough laminate flooring to cover a tread. Snap the edges together. Some will slide straight in, and others require a slight tilt. Follow the instructions with your flooring. Turn the flooring face down and place a 3/8-in. plywood tread on its back. Trace the outline onto the flooring and cut it out with a jigsaw. Repeat for each step.
Apply construction adhesive to the back of one set of flooring pieces and apply them to a plywood tread top. Measure the outside edges of this piece and cut the appropriate edge trim to fit. You can use a bullnose molding in a matching color, or find trim from the same maker as the flooring.
Check the angles of the corners with an angle finder. Place one leg of the finder on each face of the corner. The angle will be marked in the indicator. Use one-half of this angel to cut the miter for each piece. Glue the trim around the tread top, with its top edge flush with the flooring, with construction adhesive.
Place a tread base into a tray and drive the screws you removed into its edge or bottom, depending on the frame. Place a tread top on top of the base. Drive 1-1/4-inch fine-thread drywall screws up through its bottom to fasten the tread in place. Repeat for each step. Use six screws per step.