Clean your records before storing them to remove any dust that has already accumulated in the grooves. According to the authors of "Audiovisual Equipment and Materials: A Basic Repair and Maintenance Manual," the best cleaning solution is two tablespoons of liquid dish detergent mixed with 16 oz. of water. Dip a clean, lint-free cotton cloth into the soapy water, wring it out, and wash the record, following the curve of the grooves. Let the record air-dry.
Slide the record into a polyethylene liner before inserting it into the record cover. Handle the record carefully, touching only the center paper label and the very edges. This helps avoid getting oils from your skin on the record. You can buy polyethylene liners from online shops that deal in record accessories and equipment.
Place the record into its cover, and put a plastic outer sleeve over the original cover. Outer sleeves come with and without flaps that close with Velcro or a light adhesive. Those with flaps will help keep dust off of your records better than those without. As with inner liners, you can buy outer sleeves online from record equipment and accessory dealers.
Store your records vertically (not stacked horizontally), away from warm areas, and dust the storage area frequently. Dusting once a week will make a difference in keeping your LPs dust-free. Every few months, open up records you haven't played in a while and check to see if they need cleaning.