Wet a sponge, and wring it out so it's slightly damp. Do not oversaturate it with water, or it may do more damage to your couch, depending on the fabric it's made of. This method works for a microfiber, microsuede, leather or water-safe fabric couch. Sweep the sponge over the couch to pick up the cat fur.
Use fabric fixers to remove the fur. A sticky lint roller can pick fur up easily, or try rubbing a dryer sheet across the furry areas. It should cling to the dryer sheet and come right up.
Vacuum fur from the upholstery using a small vacuum cleaner or one with an attachment hose or appliance. Remove the cushions from the couch to get into the crevices with the vacuum cleaner, and remove as much of the fur as possible. This works for large clumps of fur.
Pick up any remaining fur with a standard pair of rubber cleaning gloves. Slip the gloves on, and wet them a little bit. Glide the damp gloves over the fur, and watch it stick to the damp gloves. This is a useful method if there is fur in the couch crevices or corners.