Not all insulation types are recommended for vents. In fact, most are not due to the transference of air that constantly happens in the vent system. Instead, the best material is fiberglass insulation with a strong barrier on one side. This barrier is what you install facing outward, and it prevents the insulation from blowing out of the vent system.
It is imperative that you confirm the type of original insulation before you begin removal, as some older insulation can contain potentially toxic chemicals that should never be breathed in. If this is the case, hire a professional to remove the old insulation. If you confirm that the insulation is safe, your job is to disassemble the vent tubing and pull out the old insulation. The insulation will be glued down, so expect some residue to remain.
Line the inner walls of the vent tubes with the new insulation, gluing it in place. As you work, make note of the vent outlets and cut out the squares for those areas. Be very careful to avoid tearing any holes in the insulation barrier, as these holes will only get worse and start leaking insulation over time.
Once the insulation is installed, go back and seal off the vents with caulking around the exterior of each vent. Check that the tubes are properly reconstructed and verify that the screws are tight. For extra insulation, you also can wrap the vent tubes with foam insulation on the outside.