Experts and BHG readers answer.
Remove rust with steel wool or a light sandpaper. Dirt usually comes off with just a wire brush, as you would use to clean the outdoor grill. Spray any metal parts with a lubricant oil spray to keep rust from recurring. File edges on tools to sharpen them with a metal file, in the same direction only. Use sandpaper on wooden handles; then apply linseed oil. I have also heard of people standing their tools upright in buckets of sand over the winter to keep the oil fresh and off other surfaces.