1. Talk with the manufacturer about the chemicals that are in the mattress and could be off gassing. Ask them to hold it in the warehouse for several weeks before delivering it to give the chemicals time to off-gas. And ask them for their recommendations about dealing with the fumes.
2. Take a ride with the mattress. This may seem like an incredibly silly idea, but this can make a huge impact on getting rid of the odors. Put the mattress in an open truck and take a ride with it. Having air blow through the mattress has proven to get rid of the smell quickly and permanently. You can also do this as you take delivery of the mattress.
3. If the mattress is already staring at you in your bedroom, try using a box fan in an open window (weather permitting). Turn the fan so that it pulls air from the inside of the room to the outside. Close the door to the rest of the house. Although this is a temporary solution, it might possibly help keep the air in the rest of the house tolerable.
4. Research the mattresses on the market to find out which ones use fewer chemicals. Since 2004 the Consumer Product Safety Commission has required that any mattress sold in the United States be able to withstand an open flame for 30 minutes. This sets the safety bar wonderfully high in an attempt to prevent us from dying from a fire in bed. However, make sure that you are aware of the chemicals being used to prevent that fire. So before you throw away the old mattress make sure you have all the information on the new one.