While specific details vary, there are three main methods of disposing of a mattress -- call for a bulk pickup, drop it off at a waste facility, or if it's still in good usable condition, donate it to charity.
Bulk Pickup
Many waste management and garbage companies have a bulk pickup option. You can phone and request a pickup of a mattress. In some areas, you get a free pickup within a set time period, while in others you may be charged a small fee. Some garbage companies, such as New York's Department of Sanitation, will pick up a mattress at the curb, but it must be sealed in plastic to prevent the spread of bedbugs.
Drop It Off
The local waste management agency generally has a central drop-off location for bulky items. There may be a fee. It may also sponsor specific drop-off days, where a copy of your garbage bill and photo ID allows you to drop off one or more large items at a convenient location.
Donate It
A mattress in clean, unstained condition without tears may be donated to a local charity. Call ahead before going to the donation drop-off to ensure that the charity accepts mattresses. If it's in less than perfect condition, a mattress recycling facility may accept it and recycle the metal springs, foam and wood frame.