The procedure for removing attic insulation varies depending upon the type of insulation that is existing.
Fiberglass Batts are removed by literally walking/crawling around in the attic with 50 gallon trash bags. The fiberglass batts are picked up off of the attic floor, folded up, and stuffed into trash bags. Then these bags are carried out of the home, thrown into a truck, and eventually taken to the dump to be disposed of.
Blown (fiberglass, cellulose, or other) insulation is vacuumed out of the attic with a large gas powered vacuum machine. A crew of 2-3 people is typically what is sent to perform vacuuming existing insulation from an attic. One or two people go into the attic with a long flexible hose that sucks the insulation through it. The hose is connected to a "drop box" which allows large or heavy items to fall into the box instead of going through the vacuum which could damage it. Then, one person sits in the truck and makes sure the old insulation goes into large cylindrical bags that are 5 ft. long and 4 ft. ion diameter. The bags are eventually taken to the dump and disposed of properly.
Cellulose insulation is made of recycled newspaper. The recycled newspaper is shredded and treated with chemicals that help to make it fire resistant, and to repel insects and rodents too.