You must remove loose dust as the very first step. You can use the upholstery attachment of your vacuum cleaner for this job. You should gently run the machine over the cushion surface, seams, corners, and crevices. You can clean both sides if the cushions are removable, following the manufacturer’s guide.
You must never press the vacuum nozzle too hard on soft fabrics. High friction damages the fabric threads and ruins the look. You need to be extra careful while vacuuming thin and old fabrics.
You can mix a little mild liquid soap in water for food or drink stains. You should dip a soft cloth in this mix, wring it well, and gently dab the stained area. You must not rub hard because it spreads the stain and fades the color.