Measure the dimensions of the area beneath the overhang of each of your stairs. As the area below each step may be different, it's important to measure each one individually. Note the height of the gap below the overhang and how far the overhang itself juts over the step below.
Mark pieces of scrap wood to slot into either side of the area beneath the overhang of each of your stairs. This will create a frame you can use to block the area off with your laminate boards.
Put on a pair of safety goggles and use a jigsaw to cut your wood to size.
Slot the wood you've cut into position beneath the overhang on each of your stairs. Check wooden fills are flush with the outside edge of each overhang with a vertical bubble level.
Nail or glue each piece of wood into place.
Measure the riser area of each stair and use a jigsaw to cut laminate boarding to glue over the frame you've made.