Remove a new mattress from its plastic packaging and allow it to air out for up to two weeks before sleeping on it. It is best to do this in a seldom-used room with the door closed and windows open.
Cover the mattress with a waterproof dust mite encasement. This puts a barrier between yourself and any chemicals in the mattress and also lessens reactions to allergens.
Use a wool mattress topper. Wool is a natural fiber that resists mold and regulates body heat. It will put a natural barrier between you and the mattress as well as provide comfort.
Encase the mattress in a mattress wrap. These sheets of polyethylene are the only material that completely blocks mattress off-gassing.