Gain access to the attic space directly above the vaulted ceiling.
Place a sheet of plywood across floor joists to allow entry to unfinished areas. Do not walk on unfinished floors because you will fall through the ceiling.
Lay insulation between the attic joists with the paper facing down. Begin in the far corners and work your way towards the middle to prevent walking on installed insulation. If you lack adequate working space, rent an insulation blower and blow in loose fill insulation. Place the loose fill insulation in the blower and switch the blower on to spread the insulation.
Press the batts into place end to end, firmly butted up to each other until the insulation covers the entire space. Keep the insulation 3 or 4 inches back from the edges to allow air to flow through the eave vents. Cut the insulation to fit into the space as necessary, with a utility knife.