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Make sure that the room you’re working in is well-ventilated. Open all windows and doors in the room. In addition, open windows elsewhere in your house and turn on the air conditioning to encourage cross-ventilation.  Make sure the room is not very humid or moist. By ventilating the room, you'll help the mattress dry after you use cleaners on it and will allow bad smells and chemical smells to dissipate. Before you take any steps to clean the mattress, you must remove everything from the mattress that is not part of it. This is important, as dirt, grime, and bad scents can accumulate on sheets, mattress liners, mattress protectors, and other things we commonly put on top of our mattresses.  Carefully fold your sheets up as you remove them so more dust or dirt does not fall on to the mattress. Remove any mattress protectors you may have covered it with. Take off any pieces of fabric that can be detached. Perhaps the most important way to prepare your mattress is to vacuum it completely. Without vacuuming it properly, there will be a lot of dirt and debris left on the mattress – undermining your effort to clean it.  Use an upholstery attachment with your vacuum. Systematically go back-and-forth width-wise on the mattress until you vacuum the whole thing. Use the crevice attachment to vacuum hard-to-reach places like crevices, indentations, and embroidery. Flip the mattress and vacuum the other side.
Ventilate the room. Strip the sheets and bedding. Vacuum the mattress.