Apply flooring glue of the back of the boards and place them on the steps.
How to install wood laminate flooring on stairs.
Laminate flooring installation on stairs.
Alternatively you could cover the overhang with plywood to make it level.
Once this is done measure and cut out your pieces of laminate to make tread pieces riser pieces and stair nosing.
You have to ensure that there are no gaps and spaces in the flooring and it is complete and perfect in every way.
However installing laminate flooring on your stairs is a completely different matter.
Cut the flooring boards to size using a circular saw.