Avoid storing Lego bricks in your attic. The daily temperature range and extreme heat of summer can potentially damage the bricks.
Remove all batteries from Lego electronics before medium or long term storage.
Place all metal containing pieces and electronics in an airtight container (older metal axle wheels, etc) with a bag of desiccant. Desiccant is inexpensive and can be found at hardware or hobby shops, or online.
Sticker sheets should be stored individually, in long term storage the adhesives could migrate or ooze.
Store paper instructions and stickers in polyethylene, polypropylene, or polyester bags or notebook sheet protectors. The box of bags or protectors should be clearly labeled "archival safe". Other types of plastic bags contain softeners that can damage paper in long term storage. Archival notebook sheet protectors can be found at any major office supply. Archival bags can be found at art supply stores and online. Do not store these in attics, basements, or garages! Paper is highly sensitive to humidity and temperate fluctuations.
Store Lego rubber bands in a small polypropylene bag with each set, or separately. In long term storage they will probably deteriorate. (The rubber bands are easy to replace, but the rubber softeners they contain could damage bricks if they melt). Store older tires similarly.
If you have the original boxes the Lego sets came in, keep them dry and dust-free. The original boxes in good condition can enhance the value of the sets among collectors.
For more information on long term storage, a great conservation information site is the American Library of Congress at https://www.loc.gov/preservation/
A directly related question I have is if it is OK to store bricks attached together to save space, or if this will tend to cause the bricks to lose their grip and become loose after long term storage? I suspect it is better to store them loose, unattached, in case the ABS material has a 'material memory' property.