Flip open your hot tub cover and find the zipper. It is usually on the fold and may be hidden. Unzip the cover and slide out the old foam core and plastic bag it is in. The clear plastic bag is taped and sealed to try and keep the water out. Once out remove the plastic wrap.
Measure the thickness of the old core along the two long edges. Generally there is a taper from around 3.5 inches to 3 inches. This was designed to allow rain to easily run off. Take the average of those two measurements and that is the thickness of the new core you will need. If you are lucky you can buy a sheet that is that thickness or close enough. I had to buy a 2 inch and 1.5 inch sheet and glue them together.
Lay the old water soaked hot tub core on top of the new closed cell foam core and trace the shape. This will now be used to cut the new Hot tub core to size.
I used a jig saw but almost any saw will cut the foam to fit the hot tub cover shell. Once cut I used my power sander to smooth out the edges of the new hot tub cover core.
Now reverse the first step and put the new core inside the hot tub cover. Once inside, work the cover with your hand to get a smooth and wrinkle free fit. I even used a small 2x4 to smash the edge to round it over.