Lay the laminate flooring up against the floor register opening. The vent opening should be surrounded on one side and one end with laminate flooring.
Take measurements of the vent opening's width and length with a tape measure. Add 1/4-inch to the width and length measurements to accommodate expansion of the floating laminate floor.
Measure from the last row to the closest side of the vent. Transfer the measurement to the laminate floor piece that will cover the vent. Measure from the end of the last piece of laminate to the closest end of the vent. Transfer that measurement to the piece that will cover the vent. You should end up with a hash mark as a starting point.
Transfer the length and width measurements onto the laminate from the hash mark. Trace the outline of the hole onto the laminate with the measurements and a speed square.
Drill four holes inside each corner of the tracing with a 1/2-inch hole saw. The edges of the hole should be inside the tracing of the vent on the laminate.
Cut the tracing out with a jig saw, using the corner holes, as starting points, to insert the jig saw blade.