Purchase a stain that is advertised as a "low-odor" formula, which may be water based instead of oil based. Many manufacturers now offer varieties of stain that minimize odors and chemical fumes; some are even made from natural products rather than chemicals.
Ventilate the area where the stain will be used. Keep doors and windows open at all times. When indoors, do not use air conditioning, which will recirculate the stain odors.
Stain only on a day when the weather accommodates quick drying and proper ventilation. Avoid rainy days and days that are extremely hot or cold.
Place two fans in the area -- one to blow fresh air into the room -- such as from a window -- and the other to draw air out of the room. This increases ventilation and air circulation, and keeps stain odors from lingering.
Wear a disposable face mask or respirator designed to block harmful chemical fumes, or at the very least, to minimize odor inhalation. These can be purchased at home improvement or hardware stores.
Position several bowls of vinegar around the room. Vinegar is known to absorb odors.
Take frequent breaks to go outside and get fresh air. Even if you are using a respirator or face mask, a small break from breathing through the mask is recommended for health purposes.
Run ceiling or bathroom fans in the area. Wood stain fumes rise, especially in warm air, and can linger at the top of the room. Using these fans will ventilate the area quickly and eliminate odors, as well as assist in drying the stain quickly.