Ask the company that's delivering your new mattress if they accept used mattress donations. If the company only hauls or recycles used items, they may still be able to direct you to a local resource for making donations.
Contact the Salvation Army at 1-800-728-7825. The organization has more than 2,300 drop-off centers but will also pick up the item at no cost if resources permit.
Visit DonationTown.org and click the "schedule a free donation" section. Enter your ZIP code. If the directory contains charities in your area that pick up mattress donations, you can then enter your contact information, select a charity and schedule the pickup.
Call churches, shelters and thrift stores in your community to see if they accept donations or know of any families in need of a bed.
Post an ad on free Internet boards such as CraigsList.com. Write a detailed description of it, including the size, brand, defects and any potential allergens such as pet dander or cigarette smoke. Note that it's free to anyone who needs it, and whether you require pickup or if you will arrange delivery.